Algebra

What is the value of 4y2 - y, when y = 3?

33 Remember that (4 × y × y) - y, becomes (4 × 3 × 3) - 3 or 36 - 3.

A circular pond is surrounded by a square lawn. The area (A) of the lawn is: A = 4x2 - πx2 Rearrange the formula to make 'x' the subject.

A = 4x2 - πx2 Factorise so the term with 'x's only appears once. A = x2 (4 - π) Divide both sides by 4 - π. A ÷ 4 - π = x2 Square root both sides.

What is s2 + 8s2 - 2s2?

Answer: 7s2 Remember that 1 + 8 - 2 = 7, so s2 + 8s2 - 2s2 = 7s2

Multiply out the expression: - 5(4e - 2c)

Every term in the bracket gets multiplied by -5. • -5 × 4e = -20e • -5 × -2c = 10c Therefore, -5(4e - 2c) = - 20e +10c

Multiply out 2(9y + 5)

Every term in the brackets gets multiplied by 2. • 2 × 9y = 18y • 2 × 5 = 10 2(9y + 5)= 18y + 10

A rectangle has a width of x and a length of 2x. Write down a formula for the perimeter (P) in terms of x.

P = 2x + x + 2x + x Did you remember to include all 4 sides? So P= 6x

Multiply out (a - 5)2

To work it out: Write down the expression: (a - 5)2 Expand the expression by writing it out: (a - 5) (a - 5) Everything in the first bracket is multiplied by the second bracket: a(a - 5) - 5(a - 5) Expand the brackets, by multiplying everything inside the brackets by the term outside the bracket: • a × a = a2 • a × -5 = -5a • - 5 × a = -5a • - 5 × - 5 = 25 The expression now looks like this: a2 - 5a - 5a + 25 Which can be simplified to: a2 - 10a + 25

What is 3c2 × 5c4?

To work it out: • Add the indices: • 2 + 4 = 6 • Multiply the numbers in front of the variable: • 3 x 5 = 15 • Answer: • 3c2 × 5c4 = 15c6

Simplify the expression 5x + 3y - 6x + 4y + 3z

To work it out: • Write down the expression • 5x + 3y - 6x + 4y + 3z • Collect the like terms together - i.e., re-order them • 5x - 6x + 3y + 4y + 3z • Simplify your expression, x first • 5x - 6x = -x (ie, -1x) • Then simplify y • 3y + 4y = 7y • Then simplify z • 3z The answer is: -x + 7y + 3z

Simplify this expression: x + 5 + 3x- 7 + 9x+ 3 - 4x

To work it out: • Write down the expression • x + 5 + 3x - 7 + 9x + 3 - 4x • Collect all the terms together which are alike. Remember that each term comes with an operation (+, -) which goes before it. • x + 3x + 9x - 4x + 5 - 7 + 3 • Simplify the x terms. • x + 3x + 9x - 4x = 9x • Simplify the numbers separately. • 5 - 7 + 3 = 1 Answer: x + 5 + 3x - 7 + 9x + 3 - 4x can be simplified to 9x + 1

The equation of a straight line is y = mx + c Rearrange the formula to make 'c' the subject.

y - mx = c or c = y - mx [To work this out: y = mx + c, so subtract mx from both sides.]

What is the cost of hiring this taxi for 16 miles?

£10 Remember that C = £2 + (16 x £0.50) = £2 + £8 = £10

Multiply out the following:- a(2a - 5)

• a × 2a = 2a2 • a × -5 = -5a • a(2a - 5) = 2a2 - 5a