Factoring multivariable polynomials

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This solution deals with factoring multivariable polynomials.

Solution found

2*(x+3y)^2

See steps

Step by Step Solution

Step 1 :

Equation at the end of step 1 :

  ((2 • (x²)) +  12xy) +  (2•3²y²)
 Step  2  :

Equation at the end of step 2 :

  (2x² +  12xy) +  (2•3²y²)

Step 3 :

Step 4 :

Pulling out like terms :

4.1 Pull out like factors :

2x² + 12xy + 18y² = 2 • (x² + 6xy + 9y²)

Trying to factor a multi variable polynomial :

4.2 Factoring x² + 6xy + 9y²

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

Found a factorization : (x + 3y)•(x + 3y)

Detecting a perfect square :

4.3 x² +6xy +9y² is a perfect square

It factors into (x+3y)•(x+3y)
which is another way of writing (x+3y)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 :

  2 • (x + 3y)²