Maths Expansions Exercise3-1

Expansions Exercise 3.1

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Q1 By using standard formulae, expand the following (1 to 9):
(i) (2x + 7y)²
(ii) (1/2 x + 2/3 y)²

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Q2 (i) (3x + 1/2x)²
(ii) (3x² y + 5z)²

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Q3 (i) (3x - 1/2x)²
(ii) (1/2 x - 3/2 y)²

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Q4 (i) (x + 3) (x + 5)
(ii) (x + 3) (x - 5)
(iii) (x - 7) (x + 9)
(iv) (x - 2y) (x - 3y)

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Q8 A man has certain notes of denominations Rs. 20 and Rs. 5 which amount to Rs. 380. If the number of notes of each kind is interchanged, they amount to Rs. 60 less as before. Find the number of notes of each denomination.

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Q9 (i) (3x + 1/x)³
(ii) (2x - 1)³

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Q10 Simplify the following (10 to 19):
(i) (a + b)2 + (a - b)²
(ii) (a + b)² - (a - b)²

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Q11 (i) (a + 1/a)² + (a - 1/a)²
(ii) (a + 1/a)² - (a - 1/a)²

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Q12 (i) (3x - 1)² - (3x - 2) (3x + 1)
(ii) (4x + 3y)² - (4x - 3y)² - 48xy

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Q13 (i) (7p + 9q) (7p - 9q)
(ii) (2x - 3/x) (2x + 3/x)

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Q14 (i) (2x - y + 3) (2x - y - 3)
(ii) (3x + y - 5) (3x - y - 5)

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Q15 (i) (x + 2/x - 3) (x - 2/x - 3)
(ii) (5 - 2x) (5 + 2x) (25 + 4x² )

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Q16 (i) (x + 2y + 3) (x + 2y + 7)
(ii) (2x + y + 5) (2x + y - 9)
(iii) (x - 2y - 5) (x - 2y + 3)
(iv) (3x - 4y - 2) (3x - 4y - 6)

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Q17 (i) (2p + 3q) (4p² - 6pq + 9q² )
(ii) (x + 1/x) (x² - 1 + 1/x² )

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Q18 (i) (3p - 4q) (9p² + 12pq + 16q² )
(ii) (x - 3/x) (x² + 3 + 9/x² )

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Q19 (2x + 3y + 4z) (4x² + 9y² + 16z² - 6xy - 12yz - 8zx).

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Q20 Find the product of the following:
(i) (x + 1) (x + 2) (x + 3)
(ii) (x - 2) (x - 3) (x + 4)

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Q21 Find the coefficient of x² and x in the product of (x - 3) (x + 7) (x - 4).

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Q22 If a² + 4a + x = (a + 2)² , find the value of x.

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Q23 Use (a + b)² = a² + 2ab + b² to evaluate the following:
(i) (101)²
(ii) (1003)²
(iii) (10.2)²

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Q24 Use (a - b)² = a² - 2ab - b ² to evaluate the following:
(i) (99)²
(ii) (997)²
(iii) (9.8)²

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Q25 By using suitable identities, evaluate the following:
(i) (103)³
(ii) (99)³
(iii) (10.1)³

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Q26 If 2a - b + c = 0, prove that 4a² - b 2 + c² + 4ac = 0.

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Q27 If a + b + 2c = 0, prove that a³ + b³ + 8c³ = 6abc.

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Q28 If a + b + c = 0, then find the value of a² /bc + b² /ca + c² /ab

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Q29 If x + y = 4, then find the value of x³ + y³ + 12xy - 64.

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Q30 Without actually calculating the cubes, find the values of:
(i) (27)³ + (-17)³ + (-10)³
(ii) (-28)³ + (15)³ + (13)³

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Q31 Using suitable identity, find the value of:

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Expansions Exercise 3.1

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Q1 By using standard formulae, expand the following (1 to 9):
(i) (2x + 7y)²
(ii) (1/2 x + 2/3 y)²

Q2 (i) (3x + 1/2x)²
(ii) (3x² y + 5z)²

Q3 (i) (3x - 1/2x)²
(ii) (1/2 x - 3/2 y)²

Q4 (i) (x + 3) (x + 5)
(ii) (x + 3) (x - 5)
(iii) (x - 7) (x + 9)
(iv) (x - 2y) (x - 3y)

Q5 (i) (x - 2y - z)²
(ii) (2x - 3y + 4z)²

Q6 (i) (2x + 3/x - 1)²
(ii) (2/3 x - 3/2x - 1)²

Q7 (i) (x + 2)³
(ii) (2a + b)³

Q8 A man has certain notes of denominations Rs. 20 and Rs. 5 which amount to Rs. 380. If the number of notes of each kind is interchanged, they amount to Rs. 60 less as before. Find the number of notes of each denomination.

Q9 (i) (3x + 1/x)³
(ii) (2x - 1)³

Q10 Simplify the following (10 to 19):
(i) (a + b)2 + (a - b)²
(ii) (a + b)² - (a - b)²

Q11 (i) (a + 1/a)² + (a - 1/a)²
(ii) (a + 1/a)² - (a - 1/a)²

Q12 (i) (3x - 1)² - (3x - 2) (3x + 1)
(ii) (4x + 3y)² - (4x - 3y)² - 48xy

Q13 (i) (7p + 9q) (7p - 9q)
(ii) (2x - 3/x) (2x + 3/x)

Q14 (i) (2x - y + 3) (2x - y - 3)
(ii) (3x + y - 5) (3x - y - 5)

Q15 (i) (x + 2/x - 3) (x - 2/x - 3)
(ii) (5 - 2x) (5 + 2x) (25 + 4x² )

Q16 (i) (x + 2y + 3) (x + 2y + 7)
(ii) (2x + y + 5) (2x + y - 9)
(iii) (x - 2y - 5) (x - 2y + 3)
(iv) (3x - 4y - 2) (3x - 4y - 6)

Q17 (i) (2p + 3q) (4p² - 6pq + 9q² )
(ii) (x + 1/x) (x² - 1 + 1/x² )

Q18 (i) (3p - 4q) (9p² + 12pq + 16q² )
(ii) (x - 3/x) (x² + 3 + 9/x² )

Q19 (2x + 3y + 4z) (4x² + 9y² + 16z² - 6xy - 12yz - 8zx).

Q20 Find the product of the following:
(i) (x + 1) (x + 2) (x + 3)
(ii) (x - 2) (x - 3) (x + 4)

Q21 Find the coefficient of x² and x in the product of (x - 3) (x + 7) (x - 4).

Q22 If a² + 4a + x = (a + 2)² , find the value of x.

Q23 Use (a + b)² = a² + 2ab + b² to evaluate the following:
(i) (101)²
(ii) (1003)²
(iii) (10.2)²

Q24 Use (a - b)² = a² - 2ab - b ² to evaluate the following:
(i) (99)²
(ii) (997)²
(iii) (9.8)²

Q25 By using suitable identities, evaluate the following:
(i) (103)³
(ii) (99)³
(iii) (10.1)³

Q26 If 2a - b + c = 0, prove that 4a² - b 2 + c² + 4ac = 0.

Q27 If a + b + 2c = 0, prove that a³ + b³ + 8c³ = 6abc.

Q28 If a + b + c = 0, then find the value of a² /bc + b² /ca + c² /ab

Q29 If x + y = 4, then find the value of x³ + y³ + 12xy - 64.

Q30 Without actually calculating the cubes, find the values of:
(i) (27)³ + (-17)³ + (-10)³
(ii) (-28)³ + (15)³ + (13)³

Q31 Using suitable identity, find the value of:

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Expansions Exercise 3.1

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Q1 By using standard formulae, expand the following (1 to 9): (i) (2x + 7y)2 (ii) (1/2 x + 2/3 y)2

Q2 (i) (3x + 1/2x)2 (ii) (3x2 y + 5z)2

Q3 (i) (3x - 1/2x)2 (ii) (1/2 x - 3/2 y)2

Q4 (i) (x + 3) (x + 5) (ii) (x + 3) (x - 5) (iii) (x - 7) (x + 9) (iv) (x - 2y) (x - 3y)

Q5 (i) (x - 2y - z)2 (ii) (2x - 3y + 4z)2

Q6 (i) (2x + 3/x - 1)2 (ii) (2/3 x - 3/2x - 1)2

Q7 (i) (x + 2)3 (ii) (2a + b)3

Q8 A man has certain notes of denominations Rs. 20 and Rs. 5 which amount to Rs. 380. If the number of notes of each kind is interchanged, they amount to Rs. 60 less as before. Find the number of notes of each denomination.

Q9 (i) (3x + 1/x)3 (ii) (2x - 1)3

Q10 Simplify the following (10 to 19): (i) (a + b)2 + (a - b)2 (ii) (a + b)2 - (a - b)2

Q11 (i) (a + 1/a)2 + (a - 1/a)2 (ii) (a + 1/a)2 - (a - 1/a)2

Q12 (i) (3x - 1)2 - (3x - 2) (3x + 1) (ii) (4x + 3y)2 - (4x - 3y)2 - 48xy

Q13 (i) (7p + 9q) (7p - 9q) (ii) (2x - 3/x) (2x + 3/x)

Q14 (i) (2x - y + 3) (2x - y - 3) (ii) (3x + y - 5) (3x - y - 5)

Q15 (i) (x + 2/x - 3) (x - 2/x - 3) (ii) (5 - 2x) (5 + 2x) (25 + 4x2 )

Q16 (i) (x + 2y + 3) (x + 2y + 7) (ii) (2x + y + 5) (2x + y - 9) (iii) (x - 2y - 5) (x - 2y + 3) (iv) (3x - 4y - 2) (3x - 4y - 6)

Q17 (i) (2p + 3q) (4p2 - 6pq + 9q2 ) (ii) (x + 1/x) (x2 - 1 + 1/x2 )

Q18 (i) (3p - 4q) (9p2 + 12pq + 16q2 ) (ii) (x - 3/x) (x2 + 3 + 9/x2 )

Q19 (2x + 3y + 4z) (4x2 + 9y2 + 16z2 - 6xy - 12yz - 8zx).

Q20 Find the product of the following: (i) (x + 1) (x + 2) (x + 3) (ii) (x - 2) (x - 3) (x + 4)

Q21 Find the coefficient of x2 and x in the product of (x - 3) (x + 7) (x - 4).

Q22 If a2 + 4a + x = (a + 2)2 , find the value of x.

Q23 Use (a + b)2 = a2 + 2ab + b2 to evaluate the following: (i) (101)2 (ii) (1003)2 (iii) (10.2)2

Q24 Use (a - b)2 = a2 - 2ab - b 2 to evaluate the following: (i) (99)2 (ii) (997)2 (iii) (9.8)2

Q25 By using suitable identities, evaluate the following: (i) (103)3 (ii) (99)3 (iii) (10.1)3

Q26 If 2a - b + c = 0, prove that 4a2 - b 2 + c2 + 4ac = 0.

Q27 If a + b + 2c = 0, prove that a3 + b3 + 8c3 = 6abc.

Q28 If a + b + c = 0, then find the value of a2 /bc + b2 /ca + c2 /ab

Q29 If x + y = 4, then find the value of x3 + y3 + 12xy - 64.

Q30 Without actually calculating the cubes, find the values of: (i) (27)3 + (-17)3 + (-10)3 (ii) (-28)3 + (15)3 + (13)3

Q31 Using suitable identity, find the value of:

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Q1 By using standard formulae, expand the following (1 to 9):
(i) (2x + 7y)²
(ii) (1/2 x + 2/3 y)²

Q2 (i) (3x + 1/2x)²
(ii) (3x² y + 5z)²

Q3 (i) (3x - 1/2x)²
(ii) (1/2 x - 3/2 y)²

Q4 (i) (x + 3) (x + 5)
(ii) (x + 3) (x - 5)
(iii) (x - 7) (x + 9)
(iv) (x - 2y) (x - 3y)

Q5 (i) (x - 2y - z)²
(ii) (2x - 3y + 4z)²

Q6 (i) (2x + 3/x - 1)²
(ii) (2/3 x - 3/2x - 1)²

Q7 (i) (x + 2)³
(ii) (2a + b)³

Q9 (i) (3x + 1/x)³
(ii) (2x - 1)³

Q10 Simplify the following (10 to 19):
(i) (a + b)2 + (a - b)²
(ii) (a + b)² - (a - b)²

Q11 (i) (a + 1/a)² + (a - 1/a)²
(ii) (a + 1/a)² - (a - 1/a)²

Q12 (i) (3x - 1)² - (3x - 2) (3x + 1)
(ii) (4x + 3y)² - (4x - 3y)² - 48xy

Q13 (i) (7p + 9q) (7p - 9q)
(ii) (2x - 3/x) (2x + 3/x)

Q14 (i) (2x - y + 3) (2x - y - 3)
(ii) (3x + y - 5) (3x - y - 5)

Q15 (i) (x + 2/x - 3) (x - 2/x - 3)
(ii) (5 - 2x) (5 + 2x) (25 + 4x² )

Q16 (i) (x + 2y + 3) (x + 2y + 7)
(ii) (2x + y + 5) (2x + y - 9)
(iii) (x - 2y - 5) (x - 2y + 3)
(iv) (3x - 4y - 2) (3x - 4y - 6)

Q17 (i) (2p + 3q) (4p² - 6pq + 9q² )
(ii) (x + 1/x) (x² - 1 + 1/x² )

Q18 (i) (3p - 4q) (9p² + 12pq + 16q² )
(ii) (x - 3/x) (x² + 3 + 9/x² )

Q19 (2x + 3y + 4z) (4x² + 9y² + 16z² - 6xy - 12yz - 8zx).

Q20 Find the product of the following:
(i) (x + 1) (x + 2) (x + 3)
(ii) (x - 2) (x - 3) (x + 4)

Q21 Find the coefficient of x² and x in the product of (x - 3) (x + 7) (x - 4).

Q22 If a² + 4a + x = (a + 2)² , find the value of x.

Q23 Use (a + b)² = a² + 2ab + b² to evaluate the following:
(i) (101)²
(ii) (1003)²
(iii) (10.2)²

Q24 Use (a - b)² = a² - 2ab - b ² to evaluate the following:
(i) (99)²
(ii) (997)²
(iii) (9.8)²

Q25 By using suitable identities, evaluate the following:
(i) (103)³
(ii) (99)³
(iii) (10.1)³

Q26 If 2a - b + c = 0, prove that 4a² - b 2 + c² + 4ac = 0.

Q27 If a + b + 2c = 0, prove that a³ + b³ + 8c³ = 6abc.

Q28 If a + b + c = 0, then find the value of a² /bc + b² /ca + c² /ab

Q29 If x + y = 4, then find the value of x³ + y³ + 12xy - 64.

Q30 Without actually calculating the cubes, find the values of:
(i) (27)³ + (-17)³ + (-10)³
(ii) (-28)³ + (15)³ + (13)³