example
Multiply using the Distributive Property: [latex]\left(x+3\right)\left(2{x}^{2}-5x+8\right)[/latex].
Solution
|
 |
| Distribute. |
[latex]x\color{red}{(2x^2-5x+8)}+3\color{red}{(2x^2-5x+8)}[/latex] |
| Multiply. |
[latex]2{x}^{3}-5{x}^{2}+8x+6{x}^{2}-15x+24[/latex] |
| Combine like terms. |
[latex]2{x}^{3}+{x}^{2}-7x+24[/latex] |
example
Multiply using the Vertical Method: [latex]\left(x+3\right)\left(2{x}^{2}-5x+8\right)[/latex].
Answer:
Solution
It is easier to put the polynomial with fewer terms on the bottom because we get fewer partial products this way.
|
 |
| Multiply [latex]\left(2{x}^{2}-5x+8\right)[/latex] by [latex]3[/latex]. |
[latex]6x^2-15x+24[/latex] |
| Multiply [latex]\left(2{x}^{2}-5x+8\right)[/latex] by [latex]x[/latex] . |
[latex]2x^3-5x^2+8x[/latex] |
| Add like terms. |
[latex]2x^3+x^2-7x+24[/latex] |
