🧱 See It
Multiplying a polynomial by a single term (a monomial) means distributing: every term inside the brackets gets multiplied by the term outside — exactly like distributing a number in a two-step equation, just now with variables and exponents involved too.
✏️ Draw It
2x(x + 3) distributed: the outside 2x reaches every term inside the brackets.
2x ( x + 3 )
↙↘
2x×x 2x×3
Arrow 1: 2x × x. Arrow 2: 2x × 3. Both arrows start at the outside 2x and land on a different term inside.
🔢 Write It
2x(x + 3) = 2x·x + 2x·3 = 2x² + 6x
(2x × x = 2x² using the product rule from Exponent Laws: x¹ × x¹ = x², since 1 + 1 = 2.)
For division, divide EVERY term by the same divisor:
(8x² − 4x) ÷ 4x
Divide each term separately using the quotient rule (subtract exponents) — never skip a term, whether multiplying or dividing.
💡 Worked Examples
Example 1 — Multiply: 3x(2x − 5)
3x × 2x = 6x²(coefficients3 × 2 = 6, exponents1 + 1 = 2)3x × (−5) = −15x- Answer:
6x² − 15x
Example 2 — Divide: (8x² − 4x) ÷ 4x
8x² ÷ 4x = 2x(quotient rule: coefficients8 ÷ 4 = 2, exponents2 − 1 = 1)−4x ÷ 4x = −1- Answer:
2x − 1 - Check by multiplying back:
4x(2x − 1) = 8x² − 4x✓
🧠 Quick Reference
Multiplying: distribute to EVERY term inside the brackets, using the product rule (add exponents) for the variable parts. Dividing: divide EVERY term by the same divisor, using the quotient rule (subtract exponents). Never skip a term.