Question

Find the product of the following binomials using identities:
$\left(i\right)(2x+y)(2x+y)\left(ii\right)(a^2+bc)(a^2-bc)\left(iii\right)(4x+5)(4x+9)$

Answer 1

$\left(i\right)(2x+y)(2x+y)=(2x+y{)}^2=(2x{)}^2+y^2+2\left(2x\right)\left(y\right)=4x^2+y^2+4xy$

$\left(ii\right)(a^2+bc)(a^2-bc)=\left(\right(a^2{)}^2-\left(bc{)}^2\right)=a^4-b^2{c}^2$

$\left(iii\right)(4x+5)(4x+9)=(4x{)}^2+(5+9\left)\right(4x)+5\times 9=16x^2+56x+45$