# Distributive Law

## Expanding Equations:

## Example One - Fruit Face

This fruit face has 2 oranges, 1 apple and 1 banana.

(a) Write this algebraically using variables such as *a* for apple, *b* for banana and *o* for orange.

(b) How many of each type of fruit would be in 10 fruit faces? Write this in algebra.

**Answer:**

(a) 1a + 1b + 2o

(b) 10 × (1a + 1b + 2o) = 10a + 10b + 20o

## Example Two - Bumper Cars

A bumper car manufacturer produces carnival sets, each with 5 white and 4 yellow bumper cars.

(a) Write this algebraically using variables such as *w* for a white car and *y* for a yellow car.

(b) How many of each colour would be in 3 carnival sets? Write this in algebra.

**Answer:**

(a) 5w + 4y

(b) 3 × (5w + 4y) = 15w + 12y

## Questions

Expand these expressions:

**Q1.** (3a + 4b) × 5

**Q2.** (2x + 5y) × 3

**Q3.** 5 × (4p – 2q)

**Answers**

**A1.** 15a + 20b

**A2.** 6x + 15y

**A3.** 20p – 10q

## Factorizing Equations:

Factorizing is grouping terms by their greatest common factor. It is the reverse of expanding equations.

## Example Three - Rock Concert

Each band at a gig has 3 guitars and 1 drum kit.

(a) Write this algebraically using variables such as *g* for guitar and *d* for drum kit.

(b) A mix-up has occurred with the storage of music equipment. There are 15 guitars and 5 drum kits in a van. How many bands are playing? Write this in algebra.

**Answer:**

(a) 3g + 1d

(b) 15g + 5d = 5 × (3g + 1d)

There are 5 bands playing.

## Example Four - Lego Monkey

Each Lego monkey uses 300 orange, 20 grey and 10 black blocks.

(a) Write this algebraically using variables such as *b* for black, *g* for grey and *o* for orange.

(b) How many Lego monkeys can be made from 1800 orange, 180 grey and 60 black blocks? Write this in algebra.

**Answer:**

(a) 300 *o* + 20 *g* + 10 *b*

(b) 1800 *o* + 20 *g* + 10 *b* = 6 × (300 *o* + 20 *g* + 10 *b*)

Six monkeys can be made.

## Questions

Factorize these expressions:

**Q1.** 20x + 15y

**Q2.** 14ab + 7a

**Q3.** 2xy – x

**Answers**

**A1.** 5 (4x + 3y)

**A2.** 7a (2b + 1)

**A3.** x (2y – 1)