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Archy [21]
2 years ago
7

PLEASE HELP NOW what is 9 - 4x^3 + 2x^2 + 8x^3 + 1 + 6x^2 simplified??

Mathematics
2 answers:
gulaghasi [49]2 years ago
7 0
Don’t click the links. Don’t trust it
GarryVolchara [31]2 years ago
5 0
4x^3+8x^2+10 should be correct
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Solve this problem???​
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The denominator of the first term is a difference of squares, such that

4<em>a</em> ² - <em>b</em> ² = (2<em>a</em>)² - <em>b</em> ² = (2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>)

So you can write the fractions as

(4<em>a</em> ² + <em>b</em> ²)/((2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>)) - (2<em>a</em> - <em>b</em>)/(2<em>a</em> + <em>b</em>)

Multiply through the second fraction by 2<em>a</em> - <em>b</em> to get a common denominator:

(4<em>a</em> ² + <em>b</em> ²)/((2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>)) - (2<em>a</em> - <em>b</em>)²/((2<em>a</em> + <em>b</em>) (2<em>a</em> - <em>b</em>))

((4<em>a</em> ² + <em>b</em> ²) - (2<em>a</em> - <em>b</em>)²) / ((2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>))

Expand the numerator:

(4<em>a</em> ² + <em>b</em> ²) - (2<em>a</em> - <em>b</em>)²

(4<em>a</em> ² + <em>b</em> ²) - (4<em>a</em> ² - 4<em>ab</em> + <em>b</em> ²)

4<em>ab</em>

<em />

So the original expression reduces to

4<em>ab</em> / ((2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>))

or

4<em>ab</em> / (4<em>a</em> ² - <em>b</em> ²)

upon condensing the denominator again.

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