Mathematics SKE Text - UNIT F2 Section 1 : Simplifying Expressions

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Unit F2 Section 1

Simplifying Expressions

When simplifying expressions you should group terms which contain the same varaible.

Note

x and x² must be treated as if they were different letters. You cannot add an x term to an x² term. The + and – signs go with the term which follows.

Worked Examples

Simplify each expression below.

(a)

4a + 3a + 6 + 2

The terms which involve a can be grouped. Also the 6 and 2 can be added.

4a + 3a + 6 + 2 = 7a + 8

(b)

4a + 8b − 2a + 3b

The terms involving a are considered together, and then the terms involving b.

4a + 8b − 2a + 3b	= 4a − 2a + 8b + 3b
	= 2a + 11b

(c)

x² + 5x − 8x + x² − 4

Here the x and x² must be treated as if they are different letters.

x² + 5x − 8x + x² − 4	= x² + x² + 5x − 8x − 4
	= 2x² − 3x − 4

(d)

8x + y − 4x − 6y

The different letters, x and y, must be considered in turn.

8x + y − 4x − 6y	= 8x − 4x + y − 6y
	= 4x − 5y

When a bracket is to be multiplied by a number or a letter, every term inside the bracket must be multiplied.

Remove the brackets from each expression below.

(a)

6(x + 5)

6(x + 5)	= 6 × x + 6 × 5
	= 6x + 30

(b)

3(2x + 7)

3(2x + 7)	= 3 × 2x + 3 × 7
	= 6x + 21

(c)

4(x − 3)

4(x − 3)	= 4 × x − 4 × 3
	= 4x − 12

(d)

x(x − 4)

x(x − 4)	= x × x − x × 4
	= x² − 4x

Exercises

Simplify each of these expressions.

(a)

a + 2a + 3a

(b)

3a + 2 + 4 + 6

(c)

3a + 2b + 8a + 4b

(d)

4x + 2y + 8y + y

(e)

5x + 2y + 8x − 3y

(f)

6a + 7b + 3b − 4a

(g)

4 + 6a − 3a + 2 + b

(h)

p + q + 2p − 8q + 3p

(i)

x + y − 8x + 2y

(j)

4x − 3p + 2p − 2x

(k)

7x − 4z + 8x − 5z

(l)

3z − 4x + 2z − 10x

(m)

3q − 4x + 8a − 2x + q

(n)

x + y + z − p − q − y

(o)

x + 6 + y + 4 + 2x − 3y

(p)

4x − 8q + 17x − 24q

(q)

−x + y + x + y

(r)

4x + 7y − 3x − 8y + x + y

(s)

−8x + 7y − 11x + 4y

(t)

6x − 18y + 17x − 4

(u)

x + y − 8x − 11y

(v)

4p + 8q − 8p − 4q

Remove the brackets from each expression below.

(a)

3(x + 5)

(b)

4(6 + x)

(c)

7(x + 2)

(d)

2(x + 6)

(e)

5(x + 2)

(f)

4(2x + 3)

(g)

5(3x + 2)

(h)

8(5x + 3)

(i)

7(x − 6)

(j)

8(5 − x)

(k)

4(2x − 7)

(l)

7(5x − 3)

(m)

6(3x − 5)

(n)

4(x − 2y)

(o)

5(x + 2y + 3z)

(p)

x(5 + x)

(q)

a(2 − a)

(r)

4(b − 3)

(s)

2x(x − 6)

(t)

4x(2x + 3)

(u)

3x(7 − 2x)

(v)

8x(x − 5)