Math, asked by arundhuti79, 1 month ago

(x + y) (x - y)(x2 + y2) expand​

Answers

Answered by santwanamohanty3
0

Step-by-step explanation:

(

+

)

(

)

(

2

+

2

)

(x+y)(x-y)(x^{2}+y^{2})

(x+y)(x−y)(x2+y2)

Simplify

1

Distribute

(

+

)

(

)

(

2

+

2

)

{\color{#c92786}{(x+y)(x-y)(x^{2}+y^{2})}}

(x+y)(x−y)(x2+y2)

(

2

+

2

)

(

)

+

(

2

+

2

)

(

)

{\color{#c92786}{x(x^{2}+y^{2})(x-y)+y(x^{2}+y^{2})(x-y)}}

x(x2+y2)(x−y)+y(x2+y2)(x−y)

2

Distribute

(

2

+

2

)

(

)

+

(

2

+

2

)

(

)

{\color{#c92786}{x(x^{2}+y^{2})(x-y)}}+y(x^{2}+y^{2})(x-y)

x(x2+y2)(x−y)+y(x2+y2)(x−y)

(

)

3

+

(

)

2

+

(

2

+

2

)

(

)

{\color{#c92786}{(x-y) \cdot x^{3}+x(x-y) \cdot y^{2}}}+y(x^{2}+y^{2})(x-y)

(x−y)⋅x3+x(x−y)⋅y2+y(x2+y2)(x−y)

3

Distribute

(

)

3

+

(

)

2

+

(

2

+

2

)

(

)

{\color{#c92786}{(x-y) \cdot x^{3}}}+x(x-y) \cdot y^{2}+y(x^{2}+y^{2})(x-y)

(x−y)⋅x3+x(x−y)⋅y2+y(x2+y2)(x−y)

4

3

+

(

)

2

+

(

2

+

2

)

(

)

{\color{#c92786}{x^{4}-yx^{3}}}+x(x-y) \cdot y^{2}+y(x^{2}+y^{2})(x-y)

x4−yx3+x(x−y)⋅y2+y(x2+y2)(x−y)

4

Distribute

4

3

+

(

)

2

+

(

2

+

2

)

(

)

x^{4}-yx^{3}+{\color{#c92786}{x(x-y) \cdot y^{2}}}+y(x^{2}+y^{2})(x-y)

x4−yx3+x(x−y)⋅y2+y(x2+y2)(x−y)

4

3

+

2

2

3

+

(

2

+

2

)

(

)

x^{4}-yx^{3}+{\color{#c92786}{x^{2}y^{2}-xy^{3}}}+y(x^{2}+y^{2})(x-y)

x4−yx3+x2y2−xy3+y(x2+y2)(x−y)

5

Rearrange terms

4

3

+

2

2

3

+

(

2

+

2

)

(

)

{\color{#c92786}{x^{4}-yx^{3}+x^{2}y^{2}-xy^{3}}}+y(x^{2}+y^{2})(x-y)

x4−yx3+x2y2−xy3+y(x2+y2)(x−y)

4

+

2

2

3

3

+

(

2

+

2

)

(

)

{\color{#c92786}{x^{4}+x^{2}y^{2}-xy^{3}-yx^{3}}}+y(x^{2}+y^{2})(x-y)

x4+x2y2−xy3−yx3+y(x2+y2)(x−y)

6

Distribute

4

+

2

2

3

3

+

(

2

+

2

)

(

)

x^{4}+x^{2}y^{2}-xy^{3}-yx^{3}+{\color{#c92786}{y(x^{2}+y^{2})(x-y)}}

x4+x2y2−xy3−yx3+y(x2+y2)(x−y)

4

+

2

2

3

3

+

(

)

2

+

(

)

3

x^{4}+x^{2}y^{2}-xy^{3}-yx^{3}+{\color{#c92786}{y(x-y) \cdot x^{2}+(x-y) \cdot y^{3}}}

x4+x2y2−xy3−yx3+y(x−y)⋅x2+(x−y)⋅y3

7

Distribute

4

+

2

2

3

3

+

(

)

2

+

(

)

3

x^{4}+x^{2}y^{2}-xy^{3}-yx^{3}+{\color{#c92786}{y(x-y) \cdot x^{2}}}+(x-y) \cdot y^{3}

x4+x2y2−xy3−yx3+y(x−y)⋅x2+(x−y)⋅y3

4

+

2

2

3

3

+

3

1

2

2

+

(

)

3

x^{4}+x^{2}y^{2}-xy^{3}-yx^{3}+{\color{#c92786}{yx^{3}-1x^{2}y^{2}}}+(x-y) \cdot y^{3}

x4+x2y2−xy3−yx3+yx3−1x2y2+(x−y)⋅y3

8

Rearrange terms

4

+

2

2

3

3

+

3

1

2

2

+

(

)

3

x^{4}+x^{2}y^{2}-xy^{3}-yx^{3}+{\color{#c92786}{yx^{3}-1x^{2}y^{2}}}+(x-y) \cdot y^{3}

x4+x2y2−xy3−yx3+yx3−1x2y2+(x−y)⋅y3

4

+

2

2

3

3

1

2

2

+

3

+

(

)

3

x^{4}+x^{2}y^{2}-xy^{3}-yx^{3}{\color{#c92786}{-1x^{2}y^{2}+yx^{3}}}+(x-y) \cdot y^{3}

x4+x2y2−xy3−yx3−1x2y2+yx3+(x−y)⋅y3

9

Distribute

4

+

2

2

3

3

1

2

2

+

3

+

(

)

3

x^{4}+x^{2}y^{2}-xy^{3}-yx^{3}-1x^{2}y^{2}+yx^{3}+{\color{#c92786}{(x-y) \cdot y^{3}}}

x4+x2y2−xy3−yx3−1x2y2+yx3+(x−y)⋅y3

4

+

2

2

3

3

1

2

2

+

3

+

3

1

4

x^{4}+x^{2}y^{2}-xy^{3}-yx^{3}-1x^{2}y^{2}+yx^{3}+{\color{#c92786}{xy^{3}-1y^{4}}}

x4+x2y2−xy3−yx3−1x2y2+yx3+xy3−1y4

10

Rearrange terms

4

+

2

2

3

3

1

2

2

+

3

+

3

1

4

x^{4}+x^{2}y^{2}-xy^{3}-yx^{3}{\color{#c92786}{-1x^{2}y^{2}+yx^{3}+xy^{3}-1y^{4}}}

x4+x2y2−xy3−yx3−1x2y2+yx3+xy3−1y4

4

+

2

2

3

3

1

2

2

+

3

1

4

+

3

x^{4}+x^{2}y^{2}-xy^{3}-yx^{3}{\color{#c92786}{-1x^{2}y^{2}+xy^{3}-1y^{4}+yx^{3}}}

x4+x2y2−xy3−yx3−1x2y2+xy3−1y4+yx3

11

Combine like terms

4

+

2

2

3

3

1

2

2

+

3

1

4

+

3

x^{4}+{\color{#c92786}{x^{2}y^{2}}}-xy^{3}-yx^{3}{\color{#c92786}{-1x^{2}y^{2}}}+xy^{3}-1y^{4}+yx^{3}

x4+x2y2−xy3−yx3−1x2y2+xy3−1y4+yx3

4

3

3

+

3

1

4

+

3

x^{4}{\color{#c92786}{-xy^{3}}}-yx^{3}+xy^{3}-1y^{4}+yx^{3}

x4−xy3−yx3+xy3−1y4+yx3

12

Combine like terms

4

3

3

+

3

1

4

+

3

x^{4}{\color{#c92786}{-xy^{3}}}-yx^{3}+{\color{#c92786}{xy^{3}}}-1y^{4}+yx^{3}

x4−xy3−yx3+xy3−1y4+yx3

4

3

1

4

+

3

x^{4}{\color{#c92786}{-yx^{3}}}-1y^{4}+yx^{3}

x4−yx3−1y4+yx3

13

Combine like terms

4

3

1

4

+

3

x^{4}{\color{#c92786}{-yx^{3}}}-1y^{4}+{\color{#c92786}{yx^{3}}}

x4−yx3−1y4+yx3

4

1

4

x^{4}{\color{#c92786}{-1y^{4}}}

x4−1y4

Solution

4

1

4

x^{4}-1y^{4}

x4−1y4

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