ACT Math: FOIL and Distribution - Expand Expressions Faster Than the Eye Can Blink

FOIL expands (a+b)(c+d) by multiplying four pairs. First: a×c. Outer: a×d. Inner: b×c. Last: b×d. Then combine like terms. Example: (x+3)(x+2). First: x×x=x². Outer: x×2=2x. Inner: 3×x=3x. Last: 3×2=6. Result: x²+2x+3x+6=x²+5x+6. FOIL is the fastest way to expand two binomials on the ACT and appears in 2-3 questions per section.

Why FOIL works: it ensures you multiply every term in the first binomial by every term in the second. Without FOIL, students forget the "Outer" or "Inner" terms and get wrong answers. With FOIL, the method is systematic and error-proof.

Distribution works for any expression: a(b+c)=ab+ac. Extend to trinomials: (a+b+c)(d+e)=ad+ae+bd+be+cd+ce. The key: multiply each term in the first group by each term in the second. Example: (x+2)(x²+3x+1). Distribute: x(x²+3x+1)+2(x²+3x+1)=x³+3x²+x+2x²+6x+2=x³+5x²+7x+2. Distribution is mechanical; if you apply it carefully, you get the right answer every time.

Common error: forgetting to distribute to all terms. Students multiply (x+2)(x²+3x+1) and only expand x(x²+3x+1), forgetting the +2 terms. Using distribution systematically prevents this.

Expression 1: (x+5)(x-3). FOIL: x²-3x+5x-15=x²+2x-15. Expression 2: (2x+1)(3x-2). FOIL: 6x²-4x+3x-2=6x²-x-2. Expression 3: (x+1)(x²+2x+1). Distribution: x(x²+2x+1)+1(x²+2x+1)=x³+2x²+x+x²+2x+1=x³+3x²+3x+1. Expression 4: (a+b)(c+d+e). Distribution: a(c+d+e)+b(c+d+e)=ac+ad+ae+bc+bd+be. Expressions 1 and 2 use FOIL for binomials. Expressions 3 and 4 use distribution for larger polynomials. All rely on the same principle: multiply each term by each term.

Time yourself: expand each in under 90 seconds, including simplification. If you're slower, practice FOIL or distribution until the method is automatic. Speed comes from repetition, not new math knowledge.

Approximately 3-5 ACT Math questions per section require expanding expressions (FOIL or distribution), either directly or as a step in solving larger problems. Students who know FOIL and distribution solve these in 30 seconds using the formula. Students who don't know the method either skip the problem or spend 3 minutes trying random approaches. Mastering FOIL and distribution is a pure time-saving skill with zero additional complexity.

Spend one week drilling FOIL on 20 binomial pairs and distribution on 10 polynomial products. By test day, you'll expand expressions faster than any other test-taker and gain 5-10 minutes per section to spend on hard problems.