Question

factorise using identities 4x^2-36xy+81y^2

Answer 1

STEP 1:

Equation at the end of step 1

((4 • (x2)) + 36xy) + 34y2

STEP 2 :

Equation at the end of step 2:

(22x2 + 36xy) + 34y2

STEP 3:

Trying to factor a multi variable polynomial

3.1 Factoring 4x2 + 36xy + 81y2

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

Found a factorization : (2x + 9y)•(2x + 9y)

Detecting a perfect square :

3.2 4x2 +36xy +81y2 is a perfect square

It factors into (2x+9y)•(2x+9y)

which is another way of writing (2x+9y)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 :

(2x + 9y)^2