Algebraic manipulation

Practice 5 items →

The skill Math 1 factoring sits on. Students combine like terms with integer and fractional coefficients, distribute with negative factors, expand (ax + b)(cx + d), factor out a common factor, and factor four terms by grouping.

Specification · for a parent or teacher
Part no.
expand-factor-7
Course
Advanced Math 7 · Unit 4
Realm
Structures
Difficulty
4 of 4 — Grade 7 / Math 1 core. Structure, models, proofs on the grid.
Qty
5 items

Part no. is the node's id; the realm is the kind of math; qty is how many practice items it carries.

Students can

like terms with integer and fractional coefficients; a(b+c)a(b+c) and −a(b−c)-a(b-c); (ax+b)(cx+d)(ax+b)(cx+d); factor out a common factor; factor four terms by grouping.

Ready when

expand (2x−3)(x+5)(2x-3)(x+5) and factor 6x2+9x6x^2+9x and xy+2x+3y+6xy+2x+3y+6.

Formulas

Binomial product
(ax+b)(cx+d)=acx2+(ad+bc)x+bd(ax+b)(cx+d) = acx^2 + (ad+bc)x + bd
Negative distribution
−a(b−c)=−ab+ac-a(b - c) = -ab + ac

Watch for

(x+3)(x+4)=x2+12(x+3)(x+4)=x^2+12; −2(x−5)=−2x−10-2(x-5)=-2x-10; grouping that never rearranges.

Before · requires

After · used by

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expand-factor-7

Items: expand-factor-7-01 · expand-factor-7-02 · expand-factor-7-03 · expand-factor-7-04 · expand-factor-7-05