Explore: Operations with Polynomial Expressions Solutions

When working with polynomial expressions in Algebra 2, the directions will be to simplify , but this can mean different things depending on the given problem.

Example 4

Simplify.
$(12 x^{3} - 8 x^{2} + 5 x) - (- 7 x^{2} + x + 4)$

Implement

$(12 x^{3} - 8 x^{2} + 5 x) + (7 x^{2} - x - 4)$

$12 x^{3} - x^{2} + 4 x - 4$

Explain

Distribute –1 across the second expression to change subtraction to adding the opposite
Combine like terms

Example 5

Simplify.
$(5 x - 1) (2 x^{2} + 3 x + 6)$

Implement

$\begin{matrix} 10 x^{3} & + 15 x^{2} & + 30 x \\ + & - 2 x^{2} & - 3 x & - 6 \end{matrix} \begin{matrix} 10 x^{3} & + 13 x^{2} & + 27 x & - 6 \end{matrix}$

Explain

Distribute 5x across all terms in the 2nd expression.
Distribute –1 across all terms in the 2nd expression.
Combine like terms.

Note

Expressions can be written horizontally or vertically when multiplied, or a combination as shown in Example 5.

Example 6

Simplify.
$(10 x - 3) (2 x + 5) - 4 x^{2} + 16 x$

Implement

$20 x^{2} + 50 x - 6 x - 15 - 4 x^{2} + 16 x$

$16 x^{2} + 60 x - 15$

Explain

Distribute
Combine like terms in standard form.

Note

You may reference the More to Explore to check your answers via Desmos.