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Using the identity \( (x+a)(x+b)=x^{2}+x(a+b)+a b \), find the following product. (i) \( (x+3)(x+7) \) (ii) \( (6 a+9)(6 a-5) \) (iii) \( (4 x+3 y)(4 x+5 y) \) (iv) \( (8+p q)(p q+7) \) |
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Answer» (i) (x + 3)(x + 7) = x2 + x(3 + 7) + 21 = x2 + 10x + 21 (ii) (6a + 9)(6a - 5) = (6a)2 + 6a(9 - 5) +9x - 5 = 36a2 + 24a - 45 (iii) (4x + 3y) (4x + 5y) = (4x)2 + 4x(3y + 5y) + 3y x 5y = 16x2 + 32xy + 15y2 (iv) (8 + pq)(pq + 7) = (pq + 8)(pq + 7) = (pq)2 + pq(8 + 7) + 8 x 7 = p2q2 + 15pq + 56 |
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