Question

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

Answer 1

`16x^2-24x+9`

Explanation:

Given: `(4x-3)^2`

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

• `(a+b)^2=a^2+2ab+b^2`

• `(a-b)^2=a^2-2ab+b^2`

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

So, we get:

`(4x-3)^2=(4x)^2-2*3*4x+3^2`

`=16x^2-24x+9`

Answer 2

`16x^2 - 24x +9`

Explanation:

First let

`a = 4x`

`b = -3`

we use the formula

`a^2 + 2ab + b^2`

so
`(4x)^2 + 2(4x)(-3) + (-3)^2`

the result will be

`16x^2 - 24x + 9`

Answer 3

`16x^2-24x+9`

Explanation:

Given: `(4x-3)^2`

Write as: `color(blue)((4x-3))color(green)( (4x-3) )`

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

`color(green)(color(blue)(4x)(4x-3)color(white)("ddd")color(blue)(-3)(4x-3)) larr` notice the way the minus
`color(white)("dddddddddddddddddddddddd")`followed the `color(blue)(3)`

`16x^2ubrace(-12xcolor(white)("ddd") -12x)+9`

`16x^2color(white)("dddd")-24xcolor(white)("dddd")+9`