# How do you expand (4x-3)^2?

May 29, 2018

$16 {x}^{2} - 24 x + 9$

#### Explanation:

Given: ${\left(4 x - 3\right)}^{2}$

Use the binomial theorem for the second power, which we find that:

• ${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

• ${\left(a - b\right)}^{2} = {a}^{2} - 2 a b + {b}^{2}$

Here $a = 4 x , b = 3$, and we use the second formula.

So, we get:

${\left(4 x - 3\right)}^{2} = {\left(4 x\right)}^{2} - 2 \cdot 3 \cdot 4 x + {3}^{2}$

$= 16 {x}^{2} - 24 x + 9$

May 29, 2018

$16 {x}^{2} - 24 x + 9$

#### Explanation:

First let

$a = 4 x$

$b = - 3$

we use the formula

${a}^{2} + 2 a b + {b}^{2}$

so
${\left(4 x\right)}^{2} + 2 \left(4 x\right) \left(- 3\right) + {\left(- 3\right)}^{2}$

the result will be

$16 {x}^{2} - 24 x + 9$

May 29, 2018

$16 {x}^{2} - 24 x + 9$

#### Explanation:

Given: ${\left(4 x - 3\right)}^{2}$

Write as: $\textcolor{b l u e}{\left(4 x - 3\right)} \textcolor{g r e e n}{\left(4 x - 3\right)}$

Multiply everything in the second bracket by everything in the first.

$\textcolor{g r e e n}{\textcolor{b l u e}{4 x} \left(4 x - 3\right) \textcolor{w h i t e}{\text{ddd}} \textcolor{b l u e}{- 3} \left(4 x - 3\right)} \leftarrow$ notice the way the minus
$\textcolor{w h i t e}{\text{dddddddddddddddddddddddd}}$followed the $\textcolor{b l u e}{3}$

$16 {x}^{2} \underbrace{- 12 x \textcolor{w h i t e}{\text{ddd}} - 12 x} + 9$

$16 {x}^{2} \textcolor{w h i t e}{\text{dddd")-24xcolor(white)("dddd}} + 9$