Factor [tex]3x^2y+28xy^2+32y^3[/tex] completely.

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Today at 9:35 AM
Mathematics

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Factor [tex]3x^2y+28xy^2+32y^3[/tex] completely.

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Space Space · Answer 1 · 2025-03-30T09:40:39-04:00

Space Space

Today at 9:40 AM

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

Factor out y: y(3x² + 28xy + 32y²)
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 Link

CHUMKANDI CHUMKANDI · Answer 2 · 2025-03-30T09:40:46-04:00

SOLVING STEPS...

STEP1

FACTOR OUT y FROM THE EXPRESSION

SO ITS

[tex]y \times (3x {}^{2} + 28xy + 32y {}^{2} )[/tex]

STEP2

WRITE 28y AS A SUM

STEP3

FACTOR OUT 3x2 + 24xy

SO IT'S

[tex]y \times (3x \times (x + 8y) + 4xy + 32y {}^{2} )[/tex]

STEP4

FACTOR OUT 4xy + 32y2

SO IT'S

[tex]y \times (3x \times (x + 8y) + 4y \times (x + 8y) \: )[/tex]

STEP5

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

SO THE ANSWER IS

[tex]y \times (x + 8y) \times (3x + 4y)[/tex]

GAVE ME THE BRAINLIEST IF MY ANSWER WAS HELPFUL...