SAT Mathematics Practice Test 5

Substituting ${\mathit{a}}^2+{\mathit{b}}^2$ for $\mathit{z}$ and ab for y into the expression $4\mathit{z}+8\mathit{y}$ give $4\left({\mathit{a}}^2+{\mathit{b}}^2\right)+8\mathit{a}\mathit{b}$. Multiplying ${\mathit{a}}^2+4{\mathit{b}}^2+8\mathit{a}\mathit{b}$,or eqivalently $4\left({\mathit{a}}^2+2\mathit{a}\mathit{b}+{\mathit{b}}^2\right)$.Since $\left({\mathit{a}}^2+2\mathit{a}\mathit{b}+{\mathit{b}}^2\right)={\left(\mathit{a}+\mathit{b}\right)}^2$ , it follows that $4\mathit{z}+8\mathit{y}$ is equivalent to ${\left(2\mathit{a}+2\mathit{b}\right)}^2$.
Choices A, C, and D are incorrect and likely result from errors made when substituting or factoring.