Question

(x²- 8x+12)(x²-16)÷(x²-36)(x²-4)​

Answer 1

$\large\textbf{Given} :$

$(x^{2} -8x+12)(x^{2} -16)\div (x^{2} - 36)(x^{2} -4)$

$\large\textbf{Identity Applied }:$

$(a^{2} - b^{2} )= (a+b)(a-b)$

$\large\textbf{Solution }:$

$\mathsf{\implies \frac{(x^{2}-8x+12) (x^{2} -36 )}{(x^{2} -36)(x^{2} -4)}}$

$\mathsf{\implies \frac{(x^{2}-2x-6x+12 )(x^{2} -4)}{(x^{2} -36)(x^{2}-4 )}}$

$\mathsf{\implies \frac{x(x-2)-6(x-2)(x^{2} -16)}{(x^{2}-36 )(x^{2}-4)}}$

$\mathsf{\implies \frac{(x-6)(x-2)(x^{2} -4^{2}) }{(x^2-6^2)(x^2-2^2)}}$

$\mathsf{\implies \frac{(x-6)(x-2)(x-4)(x+4)}{(x+6)(x-6)(x+2)(x-2)}}$

$\color{deeppink}{\because (a^2-b^2)=(a+b)(a-b)}$

$\mathsf{\implies \frac{(x-4)(x+4)}{(x+6)(x+2)}}$