Question

Which polynomial is equivalent to (5n+2)^2

Answer 1

Use the formula for perfect square:

$(a+b)^2=a^2+2ab+b^2.$

Then

$(5n+2)^2=(5n)^2+2\cdot 5n\cdot 2+2^2.$

Since

$(5n)^2=5^2\cdot n^2=25n^2,$

you get

$(5n+2)^2=25n^2+20n+4.$

Answer: $25n^2+20n+4.$