Question

(25 m^2-40mn+16^2)-49z^2​

Answer 1

Step by step solution :

Step 1 :

Equation at the end of step 1 :

((25 • (m2)) - 40mn) + 24n2

Step 2 :

Equation at the end of step 2 :

(52m2 - 40mn) + 24n2

Step 3 :

Trying to factor a multi variable polynomial :

3.1 Factoring 25m2 - 40mn + 16n2

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

Found a factorization : (5m - 4n)•(5m - 4n)

Detecting a perfect square :

3.2 25m2 -40mn +16n2 is a perfect square

It factors into (5m-4n)•(5m-4n)

which is another way of writing (5m-4n)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 :

(5m - 4n)2