Consider $\left(x^{2}-8x+4\right)\left(x^{2}-8x-4\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$, where $a=x^{2}-8x$ and $b=4$. Square $4$.
$$\left(x^{2}-8x\right)^{2}-16+15$$
Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x^{2}-8x\right)^{2}$.
$$\left(x^{2}\right)^{2}-16x^{2}x+64x^{2}-16+15$$
To raise a power to another power, multiply the exponents. Multiply $2$ and $2$ to get $4$.
$$x^{4}-16x^{2}x+64x^{2}-16+15$$
To multiply powers of the same base, add their exponents. Add $2$ and $1$ to get $3$.
Consider $\left(x^{2}-8x+4\right)\left(x^{2}-8x-4\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$, where $a=x^{2}-8x$ and $b=4$. Square $4$.
$$\left(x^{2}-8x\right)^{2}-16+15$$
Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x^{2}-8x\right)^{2}$.
$$\left(x^{2}\right)^{2}-16x^{2}x+64x^{2}-16+15$$
To raise a power to another power, multiply the exponents. Multiply $2$ and $2$ to get $4$.
$$x^{4}-16x^{2}x+64x^{2}-16+15$$
To multiply powers of the same base, add their exponents. Add $2$ and $1$ to get $3$.
