Mathematics • Year 10 • Unit 2 • Lesson 3
Expanding Binomials — Skill Drill
Build fluency with FOIL: First, Outer, Inner, Last — four partial products from one binomial times another. Then handle perfect squares (a + b)² = a² + 2ab + b². One worked example, one guided trace, eight independent problems.
1. I do — fully worked example
Use FOIL: First pair, Outer pair, Inner pair, Last pair. Four products, then collect.
Problem. Expand (x + 3)(x + 2).
Step 1 — First: multiply the first terms of each bracket.
x · x = x²
Reason: x times x is x², not 2x.
Step 2 — Outer: multiply the outer pair.
x · 2 = 2x
Reason: x (first bracket) × 2 (last term of second bracket).
Step 3 — Inner: multiply the inner pair.
3 · x = 3x
Reason: 3 (last of first bracket) × x (first of second bracket).
Step 4 — Last: multiply the last terms.
3 · 2 = 6
Step 5 — Sum the four partial products and collect like terms.
x² + 2x + 3x + 6 = x² + 5x + 6
Reason: 2x and 3x are like terms — combine to 5x.
Answer: (x + 3)(x + 2) = x² + 5x + 6.
2. We do — fill in the missing steps
This time it's a perfect square. Same FOIL structure, but watch the signs. 5 marks
Problem. Expand (2x − 3)².
Step 1 — Rewrite the square as a product:
(2x − 3)² = (2x − 3)(_______)
Step 2 — Apply FOIL. Compute each product (signs included):
F: (2x)(2x) = ____ x²
O: (2x)(−3) = ____ x
I: (−3)(2x) = ____ x
L: (−3)(−3) = ____ (positive!)
Step 3 — Sum the four products:
____ x² + ____ x + ____ x + ____
Step 4 — Collect the like terms (the middle two):
Middle: ____ x + ____ x = ____ x
Step 5 — Write the simplified answer:
(2x − 3)² = ________________________
3. You do — independent practice
Show every step. First four are foundation. Next two are standard. Last two are extension.
Foundation — simple FOIL
3.1 Expand (x + 4)(x + 3). 1 mark
3.2 Expand (x + 5)(x − 2). 1 mark
3.3 Expand (x − 3)(x + 5). 1 mark
3.4 Expand (x − 4)(x − 6). 1 mark
Standard — coefficients on x
3.5 Expand (2x − 1)(3x + 4). 2 marks
3.6 Expand (x + 6)². (Hint: write it as a product first.) 2 marks
Extension — push your thinking
3.7 Expand and simplify (x + 3)(x − 3). What do you notice about the middle term? 2 marks
3.8 A student writes (x + 2)² = x² + 4. In one sentence, say what the student forgot, then write the correct expansion. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do ((2x − 3)²)
Step 1: (2x − 3)(2x − 3).
Step 2: F: 4x²; O: −6x; I: −6x; L: +9.
Step 3: 4x² + −6x + −6x + 9.
Step 4: Middle: −6x + −6x = −12x.
Step 5: (2x − 3)² = 4x² − 12x + 9.
3.1 — (x + 4)(x + 3)
F: x²; O: 3x; I: 4x; L: 12. Sum: x² + 3x + 4x + 12 = x² + 7x + 12.
3.2 — (x + 5)(x − 2)
F: x²; O: −2x; I: 5x; L: −10. Sum: x² + (−2x) + 5x + (−10) = x² + 3x − 10.
3.3 — (x − 3)(x + 5)
F: x²; O: 5x; I: −3x; L: −15. Sum: x² + 5x − 3x − 15 = x² + 2x − 15.
3.4 — (x − 4)(x − 6)
F: x²; O: −6x; I: −4x; L: +24 (negative times negative). Sum: x² − 6x − 4x + 24 = x² − 10x + 24.
3.5 — (2x − 1)(3x + 4)
F: (2x)(3x) = 6x²; O: (2x)(4) = 8x; I: (−1)(3x) = −3x; L: (−1)(4) = −4.
Sum: 6x² + 8x − 3x − 4 = 6x² + 5x − 4.
3.6 — (x + 6)²
= (x + 6)(x + 6). F: x²; O: 6x; I: 6x; L: 36. Sum: x² + 6x + 6x + 36 = x² + 12x + 36.
3.7 — (x + 3)(x − 3)
F: x²; O: −3x; I: 3x; L: −9. Sum: x² − 3x + 3x − 9 = x² − 9.
The middle term cancels (−3x + 3x = 0). This is a "difference of squares" — the topic of Lesson 5.
3.8 — Why (x + 2)² ≠ x² + 4
The student forgot the middle term 2ab — they only squared each piece separately and never multiplied the two pieces together (twice).
Correct: (x + 2)² = (x + 2)(x + 2) = x² + 2x + 2x + 4 = x² + 4x + 4.