Question

Evaluate (4x2 – 100) ÷ 6(x + 5).​

Answer 1

Answer:

SOLUTION

TO DETERMINE

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

2

−100)÷6(x+5)

FORMULA TO BE IMPLEMENTED

We are aware of the identity that

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

2

−b

2

=(a+b)(a−b)

EVALUATION

Here the expression is

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

2

−100)÷6(x+5)

Now

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

2

−100

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

2

−25)

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

2

−(5)

2

](usingidentity)

= \sf{4(x + 5)(x - 5)}=4(x+5)(x−5)

Hence the given expression

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

2

−100)÷6(x+5)

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

6(x+5)

4x

2

−100

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

6(x+5)

4(x+5)(x−5)

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

6

4(x−5)

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

3

2(x−5)

FINAL ANSWER

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

(4x

2

−100)÷6(x+5)=

3

2(x−5)

Answer 2

Answer:

α^2-b^2=(a+b)

so, 4x^2-100=(2x+10) (2x-10)