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Use the given values to verify the formulae for squares of binomials. i. a = -7, b = 8 ii. a = 11,b = 3 iii. a = 2.5,b = 1.2 |
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Answer» i. (a + b)2 = (-7 + 8)2 = 12 = 1 a2 + 2ab + b2 = (-7)2 + 2 x (-7) x 8 + 82 = 49 – 112 + 64 = 1 ∴(a + b)2 = a2 + 2ab + b2 (a – b)2 = (-7 – 8)2 = (-15)2 = 225 a2 – 2ab + b2 = (-7)2 – 2 x (-7) x 8 + (8)2 = 49 + 112 + 64 = 225 ∴(a – b)2 = a2 – 2ab + b2 ii. (a + b)2 = (11 + 3)2 = 142 = 196 a2 + 2ab + b2 = 112 + 2 x 11 x 3 + 32 = 121 + 66 + 9 = 196 ∴(a + b)2 = a2 + 2ab + b2 (a – b)2 = (11 – 3)2 = 82 = 64 a2 – 2ab + b2 = 112 – 2 x 11 x 3 + 32 = 121 – 66 + 9 = 64 ∴(a – b)2 = a2 – 2ab + b2 iii. (a + b)2 = (2.5 + 1.2)2 = 3.72 = 13.69 a2 + 2ab + b2 = (2.5)2 + 2 x 2.5 x 1.2 + (1.2)2 = 6.25 + 6 + 1.44 = 13.69 ∴(a + b)2 = a2 + 2ab + b2 (a – b)2 = (2.5 – 1.2)2 = 1.32 = 1.69 a2 – 2ab + b2 = (2.5)2 – 2 x 2.5 x 1.2 + (1.2)2 = 6.25 – 6 + 1.44 = 1.69 ∴(a – b)2 = a2 – 2ab + b2 |
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