1.

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) \( (8+p q)(p q+7) \)

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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