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3 years ago

(x+y)^2 (x2+2xy+y2) pleas show all work

Mathematics

2 answers:

lakkis [162]3 years ago

7 0

Answer:

{x}^{4}+4{x}^{3}y+6{x}^{2}{y}^{2}+4x{y}^{3}+{y}^{4}x

+4x

y+6x

+4xy

Step-by-step explanation:

1 Use Square of Sum: {(a+b)}^{2}={a}^{2}+2ab+{b}^{2}(a+b)

+2ab+b

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

+2xy+y

)(x

+2xy+y

)

2 Expand by distributing sum groups.

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

+2xy+y

)+2xy(x

+2xy+y

)+y

+2xy+y

)

3 Expand by distributing terms.

{x}^{4}+2{x}^{3}y+{x}^{2}{y}^{2}+2xy({x}^{2}+2xy+{y}^{2})+{y}^{2}({x}^{2}+2xy+{y}^{2})x

+2x

y+x

+2xy(x

+2xy+y

)+y

+2xy+y

)

4 Expand by distributing terms.

{x}^{4}+2{x}^{3}y+{x}^{2}{y}^{2}+2{x}^{3}y+4{x}^{2}{y}^{2}+2x{y}^{3}+{y}^{2}({x}^{2}+2xy+{y}^{2})x

+2x

y+x

+2x

y+4x

+2xy

+2xy+y

)

5 Expand by distributing terms.

{x}^{4}+2{x}^{3}y+{x}^{2}{y}^{2}+2{x}^{3}y+4{x}^{2}{y}^{2}+2x{y}^{3}+{y}^{2}{x}^{2}+2{y}^{3}x+{y}^{4}x

+2x

y+x

+2x

y+4x

+2xy

+2y

x+y

6 Collect like terms.

{x}^{4}+(2{x}^{3}y+2{x}^{3}y)+({x}^{2}{y}^{2}+4{x}^{2}{y}^{2}+{x}^{2}{y}^{2})+(2x{y}^{3}+2x{y}^{3})+{y}^{4}x

+(2x

y+2x

y)+(x

+4x

)+(2xy

+2xy

)+y

7 Simplify.

{x}^{4}+4{x}^{3}y+6{x}^{2}{y}^{2}+4x{y}^{3}+{y}^{4}x

+4x

y+6x

+4xy

Luda [366]3 years ago

7 0

answer: x^4+4x^3 y+6x^2 y^2+4xy^3+y^4

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