Question

Find the product of (a+b) (a²-ab+b²)​

Answer 1

Answer:

The product (a + b) (a - b) (a² - ab + b²) (a² + ab + b²)

Solution :

By rearranging the terms :

[By using the identity , (a + b)(a - b) = a² – b² ]

= a⁶ - b⁶

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Answer 2

Answer:

The product of (a+b) (a²-ab+b²) is ${a}^{3} + {b}^{3}$

Step-by-step explanation:

Given,

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

We want to find the product.

$= a \times {a}^{2} - a \times ab + a \times {b}^{2} + b \times {a}^{2} - b \times ab + b \times {b}^{2}$

$= {a}^{3} - {a}^{2} b + a {b}^{2} + b {a}^{2} - a {b}^{2} + {b}^{3} \\ = {a}^{3} + {b}^{3}$

So, product of (a+b) (a²-ab+b²) is ${a}^{3} + {b}^{3}$

This is a formula of ${a}^{3} + {b}^{3}$

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

This is a problem of Algebra.

Some important Algebra formulas:

${(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} \\ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} \\ {(x + y)}^{3} = {x}^{3} + 3 {x}^{2} y + 3x {y}^{2} + {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - 3 {x}^{2} y + 3x {y}^{2} - {y}^{3} \\ {x}^{3} + {y}^{3} = {(x + y)}^{3} - 3xy(x + y) \\ {x}^{3} - {y}^{3} = {(x - y)}^{3} + 3xy(x - y) \\ {x}^{2} - {y}^{2} = (x + y)(x - y) \\ {x}^{2} + {y}^{2} = {(x - y)}^{2} + 2xy \\ {x}^{2} - {y}^{2} = {(x + y)}^{2} - 2xy \\ {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} ) \\ {x}^{3} + {y}^{3} = (x - + y)( {x}^{2} - xy + {y}^{2} )$

Know more about Algebra,

1) https://brainly.in/question/13024124

2) https://brainly.in/question/1169549

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