Simplifying Terms in Polynomial Operations

Refining a Revenue Projection Model

Simplifying $a^2 + 7b^2 - 6a^2$

Finding the Sum $(7y^2 - 2y + 9) + (4y^2 - 8y - 7)$

Finding the Sum $(7x^2 - 4x + 5) + (x^2 - 7x + 3)$

Finding the Sum $(14y^2 + 6y - 4) + (3y^2 + 8y + 5)$

Finding the Difference $(8x^2 + 3x - 19) - (7x^2 - 14)$

Finding the Difference $(9b^2 - 5b - 4) - (3b^2 - 5b - 7)$

Finding the Difference $(9w^2 - 7w + 5) - (2w^2 - 4)$

Subtracting $(p^2 + 10pq - 2q^2)$ from $(p^2 + q^2)$

Finding the Sum $(u^2 - 6uv + 5v^2) + (3u^2 + 2uv)$

Simplifying $(a^3 - a^2b) - (ab^2 + b^3) + (a^2b + ab^2)$

Simplifying $(x^3 - x^2y) - (xy^2 + y^3) + (x^2y + xy^2)$

Simplifying $(p^3 - p^2q) + (pq^2 + q^3) - (p^2q + pq^2)$

Addition of Polynomial Functions

Arrange the steps in order to simplify $(5x^2 + 3x) - (2x^2 - x)$.

When subtracting one polynomial from another, you must change the _____ of every term in the polynomial being subtracted before combining like terms.

When subtracting one polynomial from another, what is the first step?

The Commutative Property of Addition lets you reorder the terms of a polynomial so like terms can be grouped together.

Match each term to its meaning for adding and subtracting polynomials.

When you add the like terms $25x^2$ and $15x^2$, what happens to the variable part?

Explain how to subtract one polynomial from another. What extra step is needed compared to adding polynomials?

When you combine like terms, such as $3x^2$ and $5x^2$, what part of each term do you add or subtract?