(x + y) (x - y)(x2 + y2) expand
Answers
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