How do you multiply (x+5)^{2}?

Question

How do you multiply

{(x + 5)}^{2}

?

Answer 1

Squaring means multiplying a factor or term by itself,
This example is called squaring a binomial
The answer is a trinomial

{(x + 5)}^{2} = (x + 5) (x + 5)

Each term in the bracket must be multiplied by each term in the second bracket,

{(x + 5)}^{2} = x^{2} + 5 x + 5 x + 25 = x^{2} + 10 x + 25

Note: the two middle terms will ALWAYS be the same
=5x+5x=10x
Can you see the short method to get to the answer?

{(2 x - 3)}^{2} = 4 x^{2} - 12 x + 9

{(5 x^{2} - 3 y)}^{2} = 25 x^{4} - 30 x^{2} y + 9 y^{2}

Answer 2

{(x + 5)}^{2}

means (x+5)(x+5)
This is not equal to

x^{2} + 25

Each term in the first bracket must be multiplied by each term in the second bracket, so give 4 terms as a start.

(x + 5) (x + 5) = x^{2} + 5 x + 5 x + 25

= x^{2} + 10 x + 25

This is called the square of a binomial and is always in the form:

{(a x + b)}^{2} = a^{2} x^{2} + 2 a b x + b^{2}

Expert Answer