Question

a cube minus b cube

Answer 1

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

Answer:

“a” cubed minus “b” cubed:

Factoring is more like at an expression (both sides of an equation) and seeing a pattern, or recognizing something you have seen before. For example the fact that I know thirty-six is nine times four is that when I learned my times tables I learned that

$9\times 4=36$

This can also be read backwards,

$36=9\times 4$

The same is true for ${ a }^{ 3 }-{ b }^{ 3 }$.

We know that if I multiply

$(a - b)({ a }^{ 2 } + ab +{ b }^{ 2 })$

We get,

$(a-b)({ a }^{ 2 }+ab+{ b }^{ 2 })$

$={ a }^{ 3 }+{ a }^{ 2 }b+{ ab }^{ 2 }-{ ba }^{ 2 }-a{ b }^{ 2 }-{ b }^{ 3 }$

$={ a }^{ 3 }-{ b }^{ 3 }$

Reading it backwards, we get,

${ a }^{ 3 }-{ b }^{ 3 }= (a - b)({ a }^{ 2 } + ab +{ b }^{ 2 })$, which is the answer.

Answer 2

Answer:

The algebraic formula is a³ - b³ = (a - b) (a² + ab +b²).

Step-by-step explanation:

Algebraic expression:

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x³ - 2xy³.

(a - b)³ = (a - b)(a - b)(a - b)

(a - b)³ = (a² - 2ab +b²)(a - b)

(a - b)³ = a³ - 3a²b + 3ab² - b³

(a - b)³ + 3a²b - 3ab² = a³ - b³

(a - b)³ + 3ab (a - b) = a³ - b³

(a - b)[(a - b)² + 3ab] = a³ - b³

(a - b)[a² - 2ab +b² + 3ab] = a³ - b³

(a - b)(a² +ab +b²) = a³ - b³

Hence the formula for a³ - b³ is (a - b)(a² +ab +b²).

To learn more about algebraic formula, click on the below links:

https://brainly.in/question/11582445

https://brainly.in/question/12686625

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