# Use the difference-of-squares pattern to factor each of the following.

Betsy Rhone 2021-12-15 Answered
Use the difference-of-squares pattern to factor each of the following. $16{x}^{2}-25$
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levurdondishav4
Step 1
Given algebraic expression is:
$16{x}^{2}-25$
Both the terms in the above expression are in form of perfect squares.
Therefore the given algebraic expression follows difference-of-squares pattern.
Step 2
We use the identity:
${a}^{2}-{b}^{2}=\left(a+b\right)\left(a-b\right)$...(1)
Then we get,
$16{x}^{2}-25$
$={\left(4x\right)}^{2}-{\left(5\right)}^{2}$
=(4x+5)(4x-5); [using the identity (1)]
Hence is the required factorization.

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kaluitagf
$16{x}^{2}-25={\left(4x\right)}^{2}-{\left(5\right)}^{2}$
$\le ft\left\{\because {a}^{2}-{b}^{2}=\left(a+b\right)\left(a-b\right)right\right\}$
=(4x+5)(4x-5)
=(4x+5)*(4x-5)

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