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Application of Algebraic Identities

Simplify: [5z...

Question

Simplify:
$[{(5 z - 2)}^{2} + 40 z] \div (5 z + 2)$

A

$2 z + 5$

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B

$2 z - 5$

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C

$5 z - 2$

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D

$5 z + 2$

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Solution

The correct option is D
$5 z + 2$

To simplify :
$[{(5 z - 2)}^{2} + 40 z] \div (5 z + 2)$

Using the identity,
$a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ ,
$[{(5 z - 2)}^{2} + 40 z]$
$= [25 z^{2} - 20 z + 4 + 40 z]$
$= [25 z^{2} + 20 z + 4]$

On factorizing,
$25 z^{2} + 20 z + 4$ ,
we get,
$25 z^{2} + 20 z + 4$
$= {(5 z)}^{2} + 2 \times (5 z) \times 2 + 2^{2}$

On applying the identity, $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ ,
we get ,
$25 z^{2} + 20 z + 4 = {(5 z + 2)}^{2}$

So,
$[\frac{({(5 z - 2)}^{2} + 40 z)}{(5 z + 2)}] = \frac{{(5 z + 2)}^{2}}{(5 z + 2)} = 5 z + 2$

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Similar questions

Simplify:
$[{(5 z - 2)}^{2} + 40 z] \div (5 z + 2)$

\frac{({(5 z - 2)}^{2} + 40 z)}{(5 z + 2)}

$[{(5 z - 2)}^{2} + 40 z] \div (5 z + 2)$

Solve:
$[{(5 z - 2)}^{2} + 40 z] \div (5 z + 2)$

$\frac{{{(5 z - 2)}^{2} + 40 z}}{(5 z + 2)} =$

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