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Tanzania [10]
2 years ago
14

What is the quotient (125 – 8x3) ÷ (25 + 10x + 4x2)? –2x + 5 2x – 5 –2x – 5 2x + 5

Mathematics
2 answers:
juin [17]2 years ago
8 0
ANSWER

\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = - 2x+5

EXPLANATION

We have been given the quotient,

\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} }
to simplify.

We need to rewrite the numerator as difference of two cubes.

\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = \frac{ {5}^{3} - ( {2x})^{3} }{ 25 + 10x + 4 {x}^{2} }

We need to make use of the difference of cubes formula,

{a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )

We now let,
a = 5 \: and \: b = 2x

Then the numerator becomes,

\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = \frac{ (5 - 2x)(25 + 5 (2x) + {(2x)}^{2}) }{ 25 + 10x + 4 {x}^{2} }

This simplifies to,

\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = \frac{ (5 - 2x)(25 + 10x + 4 {x}^{2}) }{ 25 + 10x + 4 {x}^{2} }

We cancel out common factors to obtain,

\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = \frac{ (5 - 2x)}{ 1}

\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = 5 - 2x
Inessa [10]2 years ago
7 0

Answer:

The quotient is (5-2x)

Step-by-step explanation:

Given the expression  \frac{125-8{x}^{3}}{25+10x+4{x}^{2}}

We have to simplify the above expression to find the quotient.

\frac{125-8{x}^{3}}{25+10x+4{x}^{2}}

⇒ \frac{5^3-{2x}^{3}}{25+10x+4{x}^{2}}

By the identity

{a}^{3}-{b}^{3}=(a-b)({a}^{2}+ab+{b}^{2})

Here, a=5 and b=2x

gives  {5}^{3}-{2x}^{3}=5^2+5(2x)+(2x)^2=25+10x+4x^2

∴ expression becomes

\frac{125-8{x}^{3}}{25+10x+4{x}^{2}}=\frac{(5-2x)(25+10x+4x^2)}{25+10x+4{x}^{2}}=(5-2x)

Hence, the quotient becomes (5-2x)

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