Question

Needs solved now please!

Which is equivalent to (negative 2 m + 5 n) squared, and what type of special product is it? 4 m squared + 25 n squared; a perfect square trinomial 4 m squared + 25 n squared; the difference of squares 4 m squared minus 20 m n + 25 n squared; a perfect square trinomial 4 m squared minus 20 m n + 25 n squared; the difference of squares

Answer 1

see explanation

Explanation:

Given

(2m + 5n)² = (2m + 5n)(2m + 5n)

Each term in the second factor is multiplied by each term in the first factor, that is

2m(2m + 5n) + 5n(2m + 5n) ← distribute both parenthesis

= 4m² + 10mn + 10mn + 25n² ← collect like terms

= 4m² + 20mn + 25n² ← perfect square trinomial

Answer 2

4 m squared minus 20 m n + 25 n squared; a perfect square trinomial

Explanation:

Given expression,

(negative 2 m + 5 n) squared

`\implies (-2m+5n)^2`

By using (a+b)² = a² + 2ab + b²,

`(-2m)^2 + 2* -2m* 5n + (5n)^2`

`4m^2 - 20mn + 25n^2`

∵ A trinomial which is the square of a binomial is called a perfect square trinomial.

Thus,
`4m^2 - 20mn + 25n^2` is a perfect square trinomial.