Question

Factor xy^2+32y^3" align="absmiddle" class="latex-formula"> completely.

Answer 1

Answer:

y(3x + 4y)(x + 8y)

General Formulas and Concepts:

Alg I

• Factoring

Step-by-step explanation:

Step 1: Define expression

3x²y + 28xy² + 32y³

Step 2: Simplify

1. Factor out y:                    y(3x² + 28xy + 32y²)
2. Factor trinomial:              y(3x + 4y)(x + 8y)

• What multiplies up to 32 adds up to 28 with 3 being multiplied as a coefficient? Numbers are 4 and 8.

Answer 2

SOLVING STEPS...

STEP1

FACTOR OUT y FROM THE EXPRESSION

SO ITS

$y \times (3x {}^{2} + 28xy + 32y {}^{2} )$

STEP2

WRITE 28y AS A SUM

STEP3

FACTOR OUT 3x2 + 24xy

SO IT'S

$y \times (3x \times (x + 8y) + 4xy + 32y {}^{2} )$

STEP4

FACTOR OUT 4xy + 32y2

SO IT'S

$y \times (3x \times (x + 8y) + 4y \times (x + 8y) \: )$

STEP5

FACTOR OUT (3x × ( x + 8y ) + 4y × ( x + 8y ) )

SO THE ANSWER IS

$y \times (x + 8y) \times (3x + 4y)$

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