Question

49 y^2 + 84 yz + 36 z ^2
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Answer 1

Step-by-step explanation:

49y2+84yz+36z2

Final result :

(7y + 6z)2

Step by step solution :

Step 1 :

Equation at the end of step 1 :

((49 • (y2)) + 84yz) + (22•32z2)

Step 2 :

Equation at the end of step 2 :

(72y2 + 84yz) + (22•32z2)

Step 3 :

Trying to factor a multi variable polynomial :

3.1 Factoring 49y2 + 84yz + 36z2

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

Found a factorization : (7y + 6z)•(7y + 6z)

Detecting a perfect square :

3.2 49y2 +84yz +36z2 is a perfect square

It factors into (7y+6z)•(7y+6z)

which is another way of writing (7y+6z)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 :

1. (7y + 6z)2

Answer 2

49y² + 84yz + 36z² = (7y)² + 2*7y*6z + (6z)²

This is in the form a² + 2ab + b² = (a+b)²

So 49y² + 84yz + 36z² = (7y + 6z)²