Question

Use suitable identities to find the following products:
$(5-3x)(3+2x)$

Answer 1

$(5-3x)(3+2x)$
$=3(\frac{5}{3}-x)\times 2(\frac{3}{2}+x)$
$=6(\frac{5}{3}-x)(\frac{3}{2}+x)$
$=-6\left[(x-\frac{5}{3})(x+\frac{3}{2})\right]$
$=-6[x^2+(\frac{-5}{3}+\frac{3}{2})x+\left(\frac{-5}{3}\right)\times \left(\frac{3}{2}\right)]$
$=-6\left[(x^2+\left(\frac{-10+9}{6}\right)x-\frac{5}{2})\right]$
$=-6[x^2-\frac{x}{6}-\frac{5}{2}]=-6x^2+x+15$