MK · 8 cards

Algebraic Expressions flashcards

8 cards with the formulas, rules and traps from this lesson. Answer in your head, then flip to check.

Term · 1/8
Name the terms, coefficients and constant in $7 a^{2} - 4 b + 9$ .
Terms are the parts joined by + or −: $7 a^{2}$ , $- 4 b$ and 9. Coefficients multiply the variables: 7 and −4 (the sign belongs to the term). The constant is the term with no variable: 9.
Rule · 2/8
What are like terms, and how are they combined?
Like terms have identical variables raised to identical powers, such as $3 x y^{2}$ and $- 5 x y^{2}$ . Add the coefficients and keep the variable part: $- 2 x y^{2}$ . Terms like $x^{2}$ and x cannot be combined.
Rule · 3/8
Distributive property: what about a minus before parentheses?
$a (b + c) = ab + a c$ : multiply the outside factor by every term inside. A leading minus flips every sign inside: $8 - (2 y - 5) = 8 - 2 y + 5 = 13 - 2 y$ .
Common trap · 4/8
Evaluating $x^{2} + 3 x$ at x = −4: why use parentheses?
Write $(- 4)^{2} + 3 (- 4) = 16 - 12 = 4$ . Without parentheses you might get −16 for the square. Put every substituted value in parentheses, then follow the order of operations.
Formula · 5/8
How do you multiply two binomials (FOIL)?
Multiply each term of one binomial by each term of the other (first, outer, inner, last), then combine like terms: $(x + 4) (x - 2) = x^{2} - 2 x + 4 x - 8 = x^{2} + 2 x - 8$ .
Formula · 6/8
How does a difference of two squares factor?
$a^{2} - b^{2} = (a - b) (a + b)$ . Example: $4 x^{2} - 25 = (2 x - 5) (2 x + 5)$ . A sum of two squares, such as $x^{2} + 9$ , does not factor this way.
Common trap · 7/8
Is $(a + b)^{2}$ equal to $a^{2} + b^{2}$ ?
No. $(a + b)^{2} = a^{2} + 2 ab + b^{2}$ and $(a - b)^{2} = a^{2} - 2 ab + b^{2}$ ; the middle term 2ab is easy to drop. Test a = 1, b = 2: 9 versus 5.
Rule · 8/8
How do you simplify a rational expression safely?
Factor top and bottom, then cancel only common factors, never single terms across + or −: $\frac{x ^{2} - 4}{x - 2} = x + 2$ , valid only for x ≠ 2, since the original denominator cannot be zero.

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