Question

In the following exercises, multiply the binomials. Use any method.

$\left(y^2-4\right)\left(y+3\right)$

Short answer

The product of the given binomials is$y^3+3y^2-4y-12$

Step-by-step solution

Step 1. Given Information

The given binomials are$\left(y^2-4\right)\left(y+3\right)$

The product is to be determined using any Method.

Step 2. Multiplying the binomials

Binomials can be multiplied using three methods: the distributive property, the FOIL method and the Vertical Method.

Using the FOIL Method, the terms are multiplied in the order of First Terms, Outer Terms, Inner Terms and then Last Terms:

$$\begin{gathered} \left(y^2-4\right)\left(y+3\right)=\left(y^2\right)\left(y\right)+\left(y^2\right)\left(3\right)+\left(-4\right)\left(y\right)+\left(-4\right)\left(3\right) \\ \left(y^2-4\right)\left(y+3\right)=y^3+3y^2-4y-12 \end{gathered}$$

Step 3. Conclusion

The product of the binomials is$y^3+3y^2-4y-12$