Question

simplify and show work (x2 + 2xy + y2)(x+1)

Answer 1

x²+2xy+y²=(x+y)²

(x²+2xy+y²)(x+1)=(x+y)²(x+1)

Answer 2

Simplifying the expression $(x^2 + 2xy + y2)(x+1)$, by applying the distributive property, we would have: $\mathbf{x^3+ x^2+ 2x^2y + xy^2 + y^2 + 2xy}$

Given:

$(x^2 + 2xy + y2)(x+1)$

Required:

Simplify the expression

Thus, to simplify the expression, $(x^2 + 2xy + y2)(x+1)$, we would apply the distributive property as shown below:

$x(x^2 + 2xy + y^2)+1(x^2 + 2xy + y^2)\\\\x^3 + 2x^2y + xy^2 + x^2 + 2xy + y^2$

• Rearrange

$\mathbf{x^3+ x^2+ 2x^2y + xy^2 + y^2 + 2xy}$

Therefore, simplifying the expression $(x^2 + 2xy + y2)(x+1)$, by applying the distributive property, we would have: $\mathbf{x^3+ x^2+ 2x^2y + xy^2 + y^2 + 2xy}$

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