Question

Using suitable algebraic identities, find the product

$\left(A\right)(x+5)(x-5)$

$\left(B\right)(x-5)(x+5)$

$\left(C\right)(3x+5)(3x+5)$

$\left(D\right)(x-1)(x-6)$

Answer 1

$\left(A\right)(x+5)(x-5)=x^2-5^2$ $[\because a^2-b^2=(a-b\left)\right(a+b\left)\right]$

=$x^2-25$

$\left(B\right)(x-5)(x+5)=x^2-5^2$

$=x^2-25$

$\left(C\right)(3x+5)(3x+5)=(3x+5{)}^2$

$(3x{)}^2+5^2+2.3x.5$ $[\because (a+b{)}^2=a^2+b^2+2ab]$

$=9x^2+25+30x$

$\left(D\right)(x-1)(x-6)=x^2-6x-x+6$

$=x^2-7x+6$