Consider $\left(11-5x\right)\left(11+5x\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$. Square $11$.
$$121-\left(5x\right)^{2}+\left(5x+9\right)^{2}$$
Expand $\left(5x\right)^{2}$.
$$121-5^{2}x^{2}+\left(5x+9\right)^{2}$$
Calculate $5$ to the power of $2$ and get $25$.
$$121-25x^{2}+\left(5x+9\right)^{2}$$
Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(5x+9\right)^{2}$.
Consider $\left(11-5x\right)\left(11+5x\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$. Square $11$.
$$121-\left(5x\right)^{2}+\left(5x+9\right)^{2}$$
Expand $\left(5x\right)^{2}$.
$$121-5^{2}x^{2}+\left(5x+9\right)^{2}$$
Calculate $5$ to the power of $2$ and get $25$.
$$121-25x^{2}+\left(5x+9\right)^{2}$$
Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(5x+9\right)^{2}$.
