SPECIAL PRODUCTS: PRODUCT OF BINOMIALS
Master multiplying two binomials using 3 different methods! Study the examples carefully.
When you multiply two binomials (like (x+a)(x+b)), the result is usually a Quadratic Trinomial (a polynomial with 3 terms where the highest exponent is 2). Here are 3 ways to solve it!
FOIL tells you the exact order to multiply the terms so you don't miss anything:
• First — Multiply the first terms.
• Outer — Multiply the outer terms.
• Inner — Multiply the inner terms.
• Last — Multiply the last terms.
Example 1: (x + 4)(x + 3)
O: x · 3 = 3x
I: 4 · x = 4x
L: 4 · 3 = 12
Combine: x² + 3x + 4x + 12 → x² + 7x + 12
This is perfect for visual learners! Draw a 2x2 grid. Put the terms of the first binomial on top, and the terms of the second binomial on the side. Multiply to fill the boxes.
Example 2: (x + 5)(x + 2)
Step 1: Top-Left box (x · x) = x²
Step 2: Top-Right box (x · 2) = 2x
Step 3: Bottom-Left box (5 · x) = 5x
Step 4: Bottom-Right box (5 · 2) = 10
Combine all boxes: x² + 2x + 5x + 10 → x² + 7x + 10
You can distribute (share) each term of the first binomial to each term of the second binomial. This is the classic way!
Example 3: (2x − 1)(x + 4)
Step 2: −1(x + 4) = −x − 4
Write them together: 2x² + 8x − x − 4
Combine like terms (8x − x = 7x): → 2x² + 7x − 4
Always be careful with signs! Negative × Negative = Positive.
Example 4: (x − 6)(x − 3)
O: x · −3 = −3x
I: −6 · x = −6x
L: −6 · −3 = +18
Combine: x² − 3x − 6x + 18 → x² − 9x + 18
Example 5: (x − 5)(x − 5) or (x − 5)²
O: x · −5 = −5x
I: −5 · x = −5x
L: −5 · −5 = +25
Combine: x² − 5x − 5x + 25 → x² − 10x + 25
Read each question carefully. Apply the method you are most comfortable with. Good luck!
Mathemalupit | Interactive Math Review & Seatwork