Question

Find each of the following products: $\left(x^2-3x+7\right)\left(2x+3\right)$.

Answer 1

Find the product:

Given, $\left(x^2-3x+7\right)\left(2x+3\right)$

Multiply each term of one expression with each term of the other expression as follows,

$\left(x^2-3x+7\right)\left(2x+3\right)$ $=\left(x^2\right)\left(2x\right)-\left(3x\right)\left(2x\right)+\left(7\right)\left(2x\right)+\left(x^2\right)\left(3\right)-\left(3x\right)\left(3\right)+\left(7\right)\left(3\right)$

$=2x^3-6x^2+14x+3x^2-9x+21$

$=2x^3-6x^2+3x^2+14x-9x+21$

$=2x^3-3x^2+5x+21$

Hence, $({\mathrm{x}}^2-3\mathrm{x}+7)(2\mathrm{x}+3)$$=2x^3-3x^2+5x+21$.