Question

Factorise 64a²+49b²+112ab

Answer 1

Reformatting the input :
Changes made to your input should not affect the solution:

(1): "b2" was replaced by "b^2". 1 more similar replacement(s).

Step by step solution :
Step 1 :
Equation at the end of step 1 :
((64 • (a2)) + 112ab) + 72b2
Step 2 :
Equation at the end of step 2 :
(26a2 + 112ab) + 72b2
Step 3 :
Trying to factor a multi variable polynomial :
3.1 Factoring 64a2 + 112ab + 49b2

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

Found a factorization : (8a + 7b)•(8a + 7b)

Detecting a perfect square :
3.2 64a2 +112ab +49b2 is a perfect square

It factors into (8a+7b)•(8a+7b)
which is another way of writing (8a+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 :
(8a + 7b)2

Answer 2

64a^2 +49b^2 +112ab = (8a)^2 + (7b)^2 + 2 ☓ 8a ☓ 7b = (8a +7b)^2        [using identity a^2 + b^2 +2ab =(a+b) ^2]