Question

Which choice is equivalent to the expression below? use the FOIL method. (√x+3) (√x-4)A. x + sqrt x + 12B. x - sqrt x-12C. x-12D. x + sqrt x-12

Answer 1

`(\sqrt[]{x}+3)\cdot(\sqrt[]{x}-4)`

Having the previous product, we can apply FOIL to find an equivalent expression.

Foil stands for First, Outer, Inner and Last. The order at which the product of two binomials can be performed:

`\begin{gathered} \text{First: (}\sqrt[]{x})\cdot(\sqrt[]{x})=x \\ \text{Outer: (}\sqrt[]{x})\cdot(-4)=-4\cdot\sqrt[]{x} \\ \text{Inner: }(3)\cdot(\sqrt[]{x})=3\cdot\sqrt[]{x} \\ \text{Last}\colon(3)\cdot(-4)=-12 \end{gathered}`

Now we just need to add the products:

`x-4\cdot\sqrt[]{x}+3\cdot\sqrt[]{x}-12`

We can simplify like terms (-4√x and 3√x which give -√x:

`x-\sqrt[]{x}-12`

Option B is the correct answer