Question

Factorise:
a) 25x 2 + 80xy + 64y 2
b) 64a 3 + 27b 3 + 144a 2 b + 108ab 2

Answer 1

Answer:

Step by Step Solution

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "y2" was replaced by "y^2". 1 more similar replacement(s).

STEP 1 : Equation at the end of step 1

((25 • (x2)) + 80xy) + 26y2

STEP 2 :

Equation at the end of step 2 :

(52x2 + 80xy) + 26y2

STEP 3 : Trying to factor a multi variable polynomial

3.1 Factoring 25x2 + 80xy + 64y2

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

Found a factorization : (5x + 8y)•(5x + 8y)

Detecting a perfect square :

3.2 25x2 +80xy +64y2 is a perfect square

It factors into (5x+8y)•(5x+8y)

which is another way of writing (5x+8y)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 :

(5x + 8y)2