# Factoring multivariable polynomials

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This solution deals with factoring multivariable polynomials.

Solution found

(2x+9y)^2

## Step by Step Solution

## Step 1 :

#### Equation at the end of step 1 :

((4 • (x^{2})) + 36xy) + 3^{4}y^{2}## Step 2 :

#### Equation at the end of step 2 :

` (2`^{2}x^{2} + 36xy) + 3^{4}y^{2}

## Step 3 :

#### Trying to factor a multi variable polynomial :

3.1 Factoring 4x^{2} + 36xy + 81y^{2}

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

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

#### Detecting a perfect square :

3.2 4x^{2} +36xy +81y^{2} 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}