Question

Q1) Factorize the following using Identities:
(a) 16m^2- + 24mj+9j^2​

Answer 1

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

((16 • (m2)) - 24mn) + 32n2

STEP

2

:

Equation at the end of step

2

:

(24m2 - 24mn) + 32n2

STEP

3

:

Trying to factor a multi variable polynomial

3.1 Factoring 16m2 - 24mn + 9n2

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

Found a factorization : (4m - 3n)•(4m - 3n)

Detecting a perfect square :

3.2 16m2 -24mn +9n2 is a perfect square

It factors into (4m-3n)•(4m-3n)

which is another way of writing (4m-3n)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 :

(4m - 3n)2