Solved: "Multiply the algebraic expression using a Special Product..."

High School
Algebra
Algebra I
Algebra foundations

nemired9

Answered question

2021-12-16

Multiply the algebraic expression using a Special Product Formula, and simplify.

{(2 + y^{3})}^{2}

Answer & Explanation

Debbie Moore

Beginner2021-12-17Added 43 answers

Step 1
Given:

{(2 + y^{3})}^{2}

Step 2

{(2 + y^{3})}^{2} = 4 + y^{6} + 4 y^{3}

= 4 + {(y^{2})}^{3} + 4 y^{3}

= 4 + (y^{2} + 4 y) (y^{4} - 4 y^{3} + 16 y^{2})

enhebrevz

Beginner2021-12-18Added 25 answers

The square of a binomial.
The square of a binomial sum is first term square plus two times the product of the sums plus last term square. Here we use the FOIL method.
FOIL Method:
FOIL is a standard method of multiplying two binomials. The word is the acronym for the four terms of the product.
Given expression is

= {(2 + y^{3})}^{2}

Square of a given binomial sum

{(2 + y^{3})}^{2} = {(2)}^{2} + 2 \cdot 2 \cdot y^{3} + {(y^{3})}^{2}

First 2 times second

t e r m + t h e \prod u c t + t e r m

squared of 2 terms squared

= 4 + 4 y^{3} + y^{6}

(by using square of binomial formula)

RizerMix

Expert2021-12-29Added 656 answers

$(2 + y^{3})^{2}$
$(2 + y^{3})^{2} = 4 + y^{6} + 4 y^{3}$
$= 4 + (y^{2})^{3} + 4 y^{3}$
$= 4 + (y^{2} + 4 y) (y^{4} - 4 y^{3} + 16 y^{2})$

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