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Gelneren [198K]
3 years ago
5

What is the formula for a^3-b^3??

Mathematics
2 answers:
grandymaker [24]3 years ago
6 0

Answer:

\boxed{\mathrm{view \ explanation}}

Step-by-step explanation:

The difference of two cubes formula is given as:

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

artcher [175]3 years ago
4 0

Step-by-step explanation:

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

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

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

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

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

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

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\frac{{y}^{2}+13y-6}{{(y-1)}^{2}(y+7)}

Step-by-step explanation:

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\frac{y}{{y}^{2}-2(y)(1)+{1}^{2}}+\frac{6}{{y}^{2}+6y-7}

2)  Use Square of Difference: {(a-b)}^{2}={a}^{2}-2ab+{b}^{2}.

\frac{y}{{(y-1)}^{2}}+\frac{6}{{y}^{2}+6y-7}

3)  Factor {y}^{2}+6y-7.

1 - Ask: Which two numbers add up to 6 and multiply to -7?

-1 and 7

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(y-1)(y-7)

Outcome/Result: \frac{y}{(y-1)^2} +\frac{6}{(y-1)(y+7)}

4) Rewrite the expression with a common denominator.

\frac{y(y+7)+6(y-1)}{{(y-1)}^{2}(y+7)}

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\frac{{y}^{2}+7y+6y-6}{{(y-1)}^{2}(y+7)}

6) Collect like terms.

\frac{{y}^{2}+(7y+6y)-6}{{(y-1)}^{2}(y+7)}

7) Simplify  {y}^{2}+(7y+6y)-6y  to  {y}^{2}+13y-6y

\frac{{y}^{2}+13y-6}{{(y-1)}^{2}(y+7)}

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2 years ago
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