Algebra Simplifying and Polynomial Operations Flashcards

A complete set of practice flashcards covering simplifying algebraic expressions, combining like terms, the distributive property, multiplying binomials via FOIL and the Box Method, squaring binomials, geometric rectangle formulas, and converting factored quadratics to standard form.

What do you do if a question asks you to simplify $5x + 2 - 8x + 10$?

Combine Like Terms by grouping terms with the same letter and exponent combo, which simplifies to $-3x + 12$.

In algebra, what defines like terms?

Terms with the same letter and exponent combo.

What do you do if a question asks you to simplify $5x(8x + 10)$?

Distribute the outside term to everything inside the parentheses, yielding $40x^2 + 50x$.

What do you do if a question asks you to simplify $(5x + 2)(8x + 10)$?

Use FOIL or the Box Method to multiply the binomials and then combine like terms to get $40x^2 + 66x + 20$.

What do you do if a question asks you to simplify $(5x + 2)^2$?

Expand it to $(5x + 2)(5x + 2)$, then use FOIL or the Box Method to multiply and combine like terms to get $25x^2 + 20x + 4$.

What do you do if a question asks you to simplify $(5x + 2) - (8x + 10)$?

Distribute a $-1$ to the terms in the second parentheses, then Combine Like Terms to get $-3x - 8$.

What do you do if a question asks you to simplify $2x(5x + 2) - 4(8x + 10)$?

Distribute $2x$ to the first parentheses and $-4$ to the second parentheses, then Combine Like Terms to get $10x^2 - 28x - 40$.

What do you do if a question asks you to determine the perimeter of a rectangle?

Add all sides ($P = a + b + c + d$).

What do you do if a question asks you to determine the area of a rectangle?

Multiply the length times width ($\text{Area} = l \times w$).

What do you do if a question asks you to simplify $(5x + 2) + (-8x + 10)$?

Remove the parentheses and then Combine Like Terms, resulting in $-3x + 12$.

What do you do if a question asks you to convert $f(x) = (2x - 3)(x + 10)$ to standard form?

Use FOIL or the Box Method to multiply the binomials.

How do you use the Box Method to multiply binomials?

Multiply the top and side terms to fill in each of the boxes, then add or subtract to Combine Like Terms.

How do you use the FOIL method to multiply binomials?

Multiply First times first, Outside times outside, Inside times inside, and Last times last, then add or subtract to Combine Like Terms.