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

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

4

+4x

3

y+6x

2

y

2

+4xy

3

+y

4

Step-by-step explanation:

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

2

=a

2

+2ab+b

2

.

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

2

+2xy+y

2

)(x

2

+2xy+y

2

)

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

2

(x

2

+2xy+y

2

)+2xy(x

2

+2xy+y

2

)+y

2

(x

2

+2xy+y

2

)

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

4

+2x

3

y+x

2

y

2

+2xy(x

2

+2xy+y

2

)+y

2

(x

2

+2xy+y

2

)

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

4

+2x

3

y+x

2

y

2

+2x

3

y+4x

2

y

2

+2xy

3

+y

2

(x

2

+2xy+y

2

)

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

4

+2x

3

y+x

2

y

2

+2x

3

y+4x

2

y

2

+2xy

3

+y

2

x

2

+2y

3

x+y

4

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

4

+(2x

3

y+2x

3

y)+(x

2

y

2

+4x

2

y

2

+x

2

y

2

)+(2xy

3

+2xy

3

)+y

4

7 Simplify.

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

4

+4x

3

y+6x

2

y

2

+4xy

3

+y

4

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i

-2x-4

step-by-step explanation: