1. Combining Like Terms

• Definition: Terms are “like terms” if they have the same variable(s) raised to the same power.

  • Example: $$3x^2+5x^2=8x^2$$

  • Not like terms: $$3x^2+5x$$

• Tips for the ACT:

  • Combine coefficients, not variables.

  • Watch out for signs: $$7x-3x=4x$$

2. Expansion and Factoring

Expansion

• Use the distributive property:

  • $$a(b+c)=ab+ac$$

• For binomials:

  • $$(a+b)^2=a^2+2ab+b^2$$

  • $$(a-b)^2=a^2-2ab+b^2$$

  • $$(a+b)(a-b)=a^2-b^2$$ (difference of squares).

Factoring

• Greatest common factor (GCF):  $$6x+9=3(2x+3)$$

• Trinomials: $$x^2+5x+6=(x+2)(x+3)$$

• Difference of squares: $$x^2-16=(x-4)(x+4)$$

3. Combining and Splitting Fractions

• Common denominator:

  • $$\frac{2}{x}+\frac{1}{y}=\frac{2y+x}{xy}$$

  • $$\frac{3}{x}-\frac{1}{y}=\frac{3y-x}{xy}$$

• Simplify: Cancel factors, not terms.

  • $$\frac{x^2+3x}{x}=x+3,\quad \text{only if }x\ne0$$

• Splitting:

  • $$\frac{x+3}{x}=1+\frac{3}{x}$$

4. Modeling Real-Life Scenarios

• Translate words into algebraic expressions:

  • Five more than twice a number → $$2x+5$$

  • The product of a number and 7, decreased by 4 → $$7x-4$$

• Word problems on the ACT:

  • Motion problems: Distance = Rate × Time.

  • Cost problems: Total = (price per item)(number of items).

  • Geometry problems: Use expressions for perimeter, area, volume.

ACT Tips:

• Always simplify expressions as much as possible.

• Check for factoring opportunities—it often appears in ACT questions.

• When in doubt with word problems, define variables clearly and build step by step.

• Do all the quizzes on this topic available on the Qbank.
• Make sure to score 80% and more on the quizzes.