Question

Expand the square of a binomial(x^2+10y^2)^2

Answer 1

Remember the following formula for a squared binomial:

`(a+b)^2=a^2+2ab+b^2`

Then, for the given binomial:

`(x^2+10y^2)^2`

Use:

`\begin{gathered} a=x^2 \\ b=10y^2 \end{gathered}`

Then:

`\begin{gathered} (x^2+10y^2)^2=(x^2)^2+2(x^2)(10y^2)+(10y^2)^2 \\ =x^4+20x^2y^2+100y^4 \end{gathered}`

Therefore:

`(x^2+10y^2)^2=x^4+20x^2y^2+100y^4`