Question

Factorize completely: a2 + 14ab + 49b2 + a + 7b

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

((a2) - 14ab) + 72b2

STEP

2

:

Trying to factor a multi variable polynomial

2.1 Factoring a2 - 14ab + 49b2

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

Found a factorization : (a - 7b)•(a - 7b)

Detecting a perfect square :

2.2 a2 -14ab +49b2 is a perfect square

It factors into (a-7b)•(a-7b)

which is another way of writing (a-7b)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 :

(a - 7b)2