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(x^2 + 2xy + y^2)(x+1) A.) X^3 + 2x^2y + x^2 + y^2 +xy^2 B.) X^2 + 2xy + y^2 C.) x^3 + x^2 +2x^2y +xy^2 + y^2 + 2xy D.) x^2 + y^2 + 2xy + x + 1
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Given\[(x^2 + 2xy + y^2)(x+1)\] \[=(x^2+2xy+y^2)(x+1)\]\[=(x^2)(x)+(x^2)(1)+(2xy)(x)+(2xy)(1)+(y^2)(x)+(y^2)(1)\]\[=x^3+x^2+2x^2y+2xy+xy^2+y^2\]\[=x^3+2x^2y+xy^2+x^2+2xy+y^2\]
Meaning the answer is C.) x^3 + x^2 +2x^2y +xy^2 + y^2 + 2xy
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