Question

SIMPLIFY 4X^2-100 BY 6(X+5)

Answer 1

To simplify

$\sf \dfrac{4 {x}^{2} - 100 }{6(x + 5)}$

$\sf \bold{Identity\:\: used\:-}$

a²-b² = (a+b)(a-b)

$\sf \bold{Solution\:-}$

Take 4 common from numerator

$\sf \implies \dfrac{4 ({x}^{2} - 25) }{6(x + 5)}\\\\\sf \implies \:\dfrac{4 ({x}^{2} - 5^2) }{6(x + 5)}\\ \\ \sf use\: identity [ a^2 - b^2 = (a+b)(a-b) ] \\ \\\sf \implies\: \dfrac{4\times(x-5)(x+5)}{6(x+5)} \\ \\ \sf \implies \:\dfrac{4(x-5)}{6}\\ \\ \sf \implies \dfrac{2}{3}(x-5)$

$\sf \bold{ANSWER\::}$$\sf \bold{\dfrac{2}{3}(x-5)}$