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x^{2}+x^{2}x\left(x+1\right)^{2}
Multiply x and x to get x^{2}.
x^{2}+x^{3}\left(x+1\right)^{2}
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
x^{2}+x^{3}\left(x^{2}+2x+1\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
x^{2}+x^{5}+2x^{4}+x^{3}
Use the distributive property to multiply x^{3} by x^{2}+2x+1.
x^{2}+x^{2}x\left(x+1\right)^{2}
Multiply x and x to get x^{2}.
x^{2}+x^{3}\left(x+1\right)^{2}
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
x^{2}+x^{3}\left(x^{2}+2x+1\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
x^{2}+x^{5}+2x^{4}+x^{3}
Use the distributive property to multiply x^{3} by x^{2}+2x+1.