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\left(x^{2}+6x+9\right)\left(x-3\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.
\left(x^{2}+6x+9\right)\left(x^{2}-6x+9\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.
x^{4}-18x^{2}+81
Use the distributive property to multiply x^{2}+6x+9 by x^{2}-6x+9 and combine like terms.
\left(x^{2}+6x+9\right)\left(x-3\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.
\left(x^{2}+6x+9\right)\left(x^{2}-6x+9\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.
x^{4}-18x^{2}+81
Use the distributive property to multiply x^{2}+6x+9 by x^{2}-6x+9 and combine like terms.