Unit 2 Algebra 4 Factorise each expression completely by taking out the HCF and putting it in front of the brackets. Check your answers by expanding the brackets. a 3a2 − 9a = (a − 3) Q4a hint What is the HCF of 3 and 9? …a² and a? b 16x2 + 12x = (4x + 3) c 5a2 + 15ab d 2q³ + 8q e 84a − 12 = ( − ) f 5a2 + ab − ac = ( + − ) g y3 + y2 = ( + ) 5 Fay writes 8x2 + 16x = 2x(4x + 8). Has she factorised the expression completely? 6 Choose the correct sign, ≠ or ; a 10a2 + 20a 10a(a + 2) b 4x(x + 1) 4x2 + 5x c 81t + 9 9(9t + 1) d m2 − m m(1 − m) Q6 hint Use the identity sign ; if the two sides of the equation are the same when the brackets are completely expanded. Use the not equals sign ≠ if the two sides of the equation are not always the same when the brackets are completely expanded. Writing and using formulae 1 STEM You can use the formula F = ma to work out the force acting on an object, where F = force (newtons) m = mass (kg) a = acceleration (m/s2) Work out F when a m = 60 and a = 2 Q1a hint ma = m × a b m = 20 and a = 1.5 = 60 × 2 = newtons c m = 100 and a = −5 2 Reasoning The rectangle has base b cm and height h cm. b cm h cm h cm Q2 hint Write a word formula first, then replace the words with letters. b cm a Write a formula for P, the perimeter of the rectangle, using b and h. Simplify your answer. b Use your formula to work out the perimeter of the rectangle when b = 6 cm and h = 7 cm. 3 52 Reasoning / Real A film company pays extras an amount per day. The amount paid depends on the acting role. a Work out the total amount paid to an extra who works for i 2 days at £50 per day ii 10 days at £35 per day. Q3b hint A formula will b Write a formula for T, the total amount paid, at £a, always have an equals sign. for d days. T = d lots of £a = c Use your formula to work out the total amount paid to an extra who works for 3 days at £25.50 per day.