2021-12-27

Multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form.
(5x - 3)(5x + 3)

Beverly Smith

Expert

Step 1
Given expression:
(5x - 3)(5x + 3)
Step 2
We know that $\left(a+b\right)\left(a-b\right)={a}^{2}-{b}^{2}$
$\left(5x-3\right)\left(5x+3\right)={\left(5x\right)}^{2}-{3}^{2}$
$\left(5x-3\right)\left(5x+3\right)=25{x}^{2}-9$

ol3i4c5s4hr

Expert

(5x-3)(5x=3)
Use the special product $\left(a-b\right)\left(a+b\right)={a}^{2}-{b}^{2}$, so
$\left(5x-3\right)\left(5x+3\right)={\left(5x\right)}^{2}-{\left(-3\right)}^{2}$
Simplify
$\left(5x-3\right)\left(5x+3\right)=25{x}^{2}-9$
Result:
$25{x}^{2}-9$

Vasquez

Expert

Given product is (5x-3)(5x+3)
It is the product of sum and difference of two terms
$\left(a+b\right)\left(a-b\right)={a}^{2}-{b}^{2}$
To find the given product use the above formula
$\left(5x-3\right)\left(5x+3\right)=\left(5x{\right)}^{2}-{3}^{2}$
$=25{x}^{2}-9$
Hence the required product is $25{x}^{2}-9$

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