SAT Mathematics Practice Test 2

If a polynomial expression is in the form ${\left(\mathit{x}\right)}^2+2\left(\mathit{x}\right)\left(\mathit{y}\right)+{\left(\mathit{y}\right)}^2$,then it is equivalent to ${\left(\mathit{x}+\mathit{y}\right)}^2$.Because ,it cab be re written as ${\left(3{\mathit{a}}^2+2{\mathit{b}}^2\right)}^2$
Choice B is incorrect. The expression ${\left(3\mathit{a}+2{\mathit{b}}^2\right)}^2$ is equivalent to the product $\left(3\mathit{a}+2\mathit{b}\right)\left(3\mathit{a}+2\mathit{b}\right)\left(3\mathit{a}+2\mathit{b}\right)\left(3\mathit{a}+2\mathit{b}\right)$.This product will contain the term $4{\left(3\mathit{a}\right)}^3\left(2\mathit{b}\right)=216{\mathit{a}}^3\mathit{b}$.However, the given polynomial, $9{\mathit{a}}^4+12{\mathit{a}}^2{\mathit{b}}^2+4{\mathit{b}}^4$ does not contain the term $216{\mathit{a}}^3\mathit{b}$.Therefore,.Choice C is incorrect. The expression $\left(9{\mathit{a}}^2+4{\mathit{b}}^2\right)$.This product will contain the terms $\left(9{\mathit{a}}^2\right)\left(9{\mathit{a}}^2\right)=81{\mathit{a}}^4$.However, the given polynomial, $9{\mathit{a}}^4+12{\mathit{a}}^2{\mathit{b}}^2+4{\mathit{b}}^4$ does not contain the term $81{\mathit{a}}^4$,Therefore $9{\mathit{a}}^4+12{\mathit{a}}^2{\mathit{b}}^2+4{\mathit{b}}^4\ne {\left(9{\mathit{a}}^2+4{\mathit{b}}^2\right)}^2$
Choice D is incorrect. The expression ${\left(9\mathit{a}+4\mathit{b}\right)}^4$ is equivalent to the product $\left(9\mathit{a}+4\mathit{b}\right)\left(9\mathit{a}+4\mathit{b}\right)\left(9\mathit{a}+4\mathit{b}\right)\left(9\mathit{a}+4\mathit{b}\right)$ This product will contain the term $\left(9\mathit{a}\right)\left(9\mathit{a}\right)\left(9\mathit{a}\right)\left(9\mathit{a}\right)=6,561{\mathit{a}}^4$.However, the given polynomial,$9{\mathit{a}}^4+12{\mathit{a}}^2{\mathit{b}}^2+4{\mathit{b}}^4$, does not contain the term $6,561{\mathit{a}}^4$ Therefore,$9{\mathit{a}}^4+12{\mathit{a}}^2{\mathit{b}}^2+4{\mathit{b}}^4\ne {\left(9\mathit{a}+4\mathit{b}\right)}^4$