Question

How do you simplify `(2ax + 1/2bx)^2`?

Answer 1

`color(magenta)((x^2(16a^2+8ab+b^2))/4`

Explanation:

`(2ax+1/2bx)^2`

`color(white)(aaaaaaaaaaaaa)` `2ax+1/2bx`
`color(white)(aaaaaaaaaaa)` `xx underline(2ax+1/2bx)`
`color(white)(aaaaaaaaaaaaa)` `4a^2x^2+abx^2`
`color(white)(aaaaaaaaaaaaaaaaaaaa)` `abx^2+1/4b^2x^2`
`color(white)(aaaaaaaaaaaaa)` `overline(4a^2x^2+2abx^2+1/4b^2x^2)`

`color(white)(aaaaaaaaaaaaa)` `:.=(4a^2x^2+2abx^2+1/4b^2x^2)xx4/4`

`color(white)(aaaaaaaaaaaaa)` `:.=(16a^2x^2+8abx^2+b^2x^2)/4`

`color(white)(aaaaaaaaaaaaa)` `:.color(magenta)(=(x^2(16a^2+8ab+b^2))/4`