Stage 8 - Q1 - 2 marks
Expand.
Hint
Distribute the whole outside factor, including its sign.
Stage 8 - Q2 - 2 marks
Expand.
Hint
Distribute the whole outside factor, including its sign.
Stage 8 - Q3 - 3 marks
Expand.
Hint
Distribute the whole outside factor, including its sign.
Stage 8 - Q4 - 3 marks
Expand.
Hint
Distribute the whole outside factor, including its sign.
Stage 8 - Q5 - 4 marks
Expand and collect like terms.
Hint
Distribute the whole outside factor, including its sign.
Stage 8 - Q6 - 4 marks
Expand and collect like terms.
Hint
Distribute the whole outside factor, including its sign.
Stage 8 - Q7 - 5 marks
Find the constant k so that \(4(2x+k)-3x=5x+28\) for every x.
Hint
An identity requires the constant terms to agree as well as the x terms.
Stage 8 - Q8 - 5 marks
Show that \(7(x+2)-7(x-3)\) has the same value for every x. Find that value.
Hint
Distribute the negative outside factor to both terms.
Stage 8 - Q9 - 5 marks
Can integers a, b make \(a(2x-1)+b(x+3)=7x+1\) for every x? Justify your answer.
Hint
Compare coefficients and constants, then check whether the resulting values are integers.
Stage 8 - Q10 - 5 marks
Choose integers a and b so that \(a(x+3)+b(x-2)\) is the constant 20 for every x. Find a and b and explain why.
Hint
For an expression to be constant, its x terms must cancel.