Find the following products using the identity : (x+a)(x+b)= $x^{2} + (a + b) x + a b .$
1. (x+2)(x+3)
2.(x-10)(x+8)
3.(x+15)(x-6)
4. (x+7)(x+7)

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Solution

$(x + a) (x + b) = x^{2} + (a + b) x + a b$
(i) $(x + 2) (x + 3)$
$= x^{2} + (2 + 3) x + 2 \times 3$
$= x^{2} + 5 x + 6$
(ii) $(x - 10) (x + 8)$
$= x^{2} + (- 10 + 8) x + (- 10) \times 8$
$= x^{2} - 2 x - 80$
(iii) $(x + 15) (x - 6)$
$= x^{2} + (15 - 6) x + 15 \times (- 6)$
$= x^{2} + 9 x - 90$
(iv) $(x + 7) (x + 7)$
$= x^{2} + (7 + 7) x + 7 \times 7$
$= x^{2} + 14 x + 49$ .

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