Lauren Mullins

2022-02-11

How do you find the product ${\left(3c+4d\right)}^{2}$?

patriette65s

${\left(3c+4d\right)}^{2}$
$=\left(3c+4d\right)×\left(3c+4d\right)$
$=3c×\left(3c+4d\right)+4d×\left(3c+4d\right)$
$=3c×3c+3c×4d+4d×3c+4d×4d$
$=9{c}^{2}+24cd+16{d}^{2}$

Layla Humphrey

Explanation:
Using the special product ${\left(a+b\right)}^{2}={a}^{2}+2ab+{b}^{2}$, we can set a=3c and b=4d to get
${\left(3c+4d\right)}^{2}={\left(3c\right)}^{2}+2\left(3c\right)\left(4d\right)+{\left(4d\right)}^{2}$
$={3}^{2}{c}^{2}+\left(2\right)\left(3\right)\left(4\right)cd+{4}^{2}{d}^{2}$
$=9{c}^{2}+24cd+16{d}^{2}$

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