Question

Find the product using the identity (x+a)(x+b)=x²+(a+b)x+ab
____________

(i) (x+7)(x+5)

(ii) (7x+2y)(7x+6y)

(iii) 98 × 97
____________

NO SPAM PLEASE ​

Answer 1

$\huge \boxed { \colorbox{gray}{solution \: : }}$

_______________________

[1]~ ( x + 7 ) ( x + 5 )

$= {x}^{2} + (7 + 5)x + 7 \times 5 \\ \tt\bf = {x}^{2} + 12x + 35$

_______________________

[2]~ ( 7x + 2y ) ( 7x + 6y )

$= (7x) {}^{2} + (2y + 6y)(7x) + (2y) \times (6y) \\ = {49x}^{2} + (8y)(7x) + 12y {}^{2} \: \: \: \: \: \: \: \: \\ \tt \bf = 49x {}^{2} + 56xy + 12y {}^{2}$

_______________________

[3]~ 98 × 97

$= (100 - 2) \times (100 - 3) \\ = {(100)}^{2} + ( - 2 - 3) \times 100 + ( - 2) \times ( - 3) \\ = 10000 - 500 + 6 \\ = 10006 - 500 \\ \tt \bf = 9506$