Question

What is (1+2x3) squared

Answer 1

`\large\boxed{(1+2x^3)^2=4x^6+4x^3+1}`

Explanation:

`(1+2x^3)^2\\\\\bold{METHOD\ 1:}\\\\(1+2x^3)^2=(1+2x^3)(1+2x^3)\qquad\text{use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(1)(1)+(1)(2x^3)+(2x^3)(1)+(2x^3)(2x^3)\\\\=1+2x^3+2x^3+4x^6\qquad\text{combine like terms}\\\\=1+4x^3+4x^6`

`\bold{METHOD\ 2:}\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(1+2x^3)^2=1^2+2(1)(2x^3)+(2x^3)^2\\\\=1+4x^3+2^2(x^3)^2\\\\=1+4x^3+4x^6`