Question

divide : (4x²- 100) ÷ 6(x+5)​

Answer 1

SOLUTION

TO DETERMINE

$\sf{( \: 4 {x}^{2} - 100 \: ) \div \: 6( \:x + 5 \: ) }$

FORMULA TO BE IMPLEMENTED

We are aware of the identity that

$\sf{ {a}^{2} - {b}^{2} = (a + b)(a - b) }$

EVALUATION

Here the expression is

$\sf{( \: 4 {x}^{2} - 100 \: ) \div \: 6( \:x + 5 \: ) }$

Now

$\sf{4 {x}^{2} - 100 \: }$

$= \sf{4( \: {x}^{2} - 25 \: )}$

$= \sf{4 \bigg[ \: {(x)}^{2} - {(5)}^{2} \: \bigg]} \: \: ( \: using \: identity)$

$= \sf{4(x + 5)(x - 5)}$

Hence the given expression

$= \sf{( \: 4 {x}^{2} - 100 \: ) \div \: 6( \:x + 5 \: ) }$

$\displaystyle \sf{ = \frac{4 {x}^{2} - 100 }{6(x + 5)} }$

$\displaystyle \sf{ = \frac{4 (x + 5)(x - 5) }{6(x + 5)} }$

$\displaystyle \sf{ = \frac{4 (x - 5) }{6} }$

$\displaystyle \sf{ = \frac{2 (x - 5) }{3} }$

FINAL ANSWER

$\boxed{ \: \displaystyle \sf{ (4 {x}^{2} - 100 \: ) \div \: 6( \:x + 5 \: ) = \frac{2 (x - 5) }{3} } \: }$

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Answer 2

2(x-5)/3 because we have divided