Question

$factorise \: 100 {x}^{2} - 80xy + 16 {y}^{2}$
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Answer 1

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Step by Step Solution...

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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).

STEP1:

Equation at the end of step 1

((100 • (x2)) - 80xy) + 24y2

STEP 2 :

Equation at the end of step2:

((22•52x2) - 80xy) + 24y2

STEP3:

STEP4:

Pulling out like terms

4.1 Pull out like factors :

100x2 - 80xy + 16y2 = 4 • (25x2 - 20xy + 4y2)

Trying to factor a multi variable polynomial :

4.2 Factoring 25x2 - 20xy + 4y2

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

Found a factorization : (5x - 2y)•(5x - 2y)

Detecting a perfect square :

4.3 25x2 -20xy +4y2 is a perfect square

It factors into (5x-2y)•(5x-2y)

which is another way of writing (5x-2y)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 :

4 • (5x - 2y)2