Question

5) Factorise - 16 m2-40mn + 25 na​

Answer 1

Answer:

 (4m - 5n)2

Step-by-step explanation:

step 1

 ((16 • (m2)) -  40mn) +  52n2

step 2

24m2 -  40mn) +  52n2

step 3

3.1    Factoring    16m2 - 40mn + 25n2  

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

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

step 4

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

It factors into  (4m-5n)•(4m-5n)

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