nemired9

2021-12-16

Multiply the algebraic expression using a Special Product Formula, and simplify.
${\left(2+{y}^{3}\right)}^{2}$

Debbie Moore

Expert

Step 1
Given:
${\left(2+{y}^{3}\right)}^{2}$
Step 2
${\left(2+{y}^{3}\right)}^{2}=4+{y}^{6}+4{y}^{3}$
$=4+{\left({y}^{2}\right)}^{3}+4{y}^{3}$
$=4+\left({y}^{2}+4y\right)\left({y}^{4}-4{y}^{3}+16{y}^{2}\right)$

enhebrevz

Expert

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 $={\left(2+{y}^{3}\right)}^{2}$
Square of a given binomial sum
${\left(2+{y}^{3}\right)}^{2}={\left(2\right)}^{2}+2\cdot 2\cdot {y}^{3}+{\left({y}^{3}\right)}^{2}$
First 2 times second squared of 2 terms squared
$=4+4{y}^{3}+{y}^{6}$ (by using square of binomial formula)

RizerMix

Expert

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

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