Question

m^2-4mn+4n^2

Answer 1

step 1
rewrite 4n^2 as 2^2n^2

Equation at the end of step 1 : ((m²) - 4mn) + 2²n² Step 2 : Trying to factor a multi variable polynomial :

2.1 Factoring m² - 4mn + 4n²

Try to factor this multi-variable trinomial using trial and error

Found a factorization : (m - 2n)•(m - 2n)

Detecting a perfect square :

2.2 m² -4mn +4n² is a perfect square

It factors into (m-2n)•(m-2n)
which is another way of writing (m-2n)²

How to recognize a perfect square trinomial:

• It has three terms

• Two of its terms are perfect squares themselves

• The remaining term is twice the product of the square roots of the other two terms

Final result : (m - 2n)²