Higher June 2017 Paper 1 Q26
26 Expand and simplify \(\qquad (x - 4)(2x + 3y)^2\) [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(4x^2 + 6xy + 6xy + 9y^2\) | M1 | oe Allow one error Implied by \(4x^2 + 12xy + \ldots\) or \(\ldots + 12xy + 9y^2\) |
| \(4x^2 + 6xy + 6xy + 9y^2\) or \(4x^2 + 12xy + 9y^2\) | A1 | oe Fully correct |
| \(4x^3 + 6x^2y + 6x^2y + 9xy^2\) or \(4x^3 + 12x^2y + 9xy^2\) or \(-16x^2 - 24xy - 24xy - 36y^2\) or \(-16x^2 - 48xy - 36y^2\) | M1dep | oe ft correct multiplication of their expansion by \(x\) or by \(-4\) if their expansion for first M1 has at least 3 terms after simplification |
| \(4x^3 + 12x^2y + 9xy^2 - 16x^2 - 48xy - 36y^2\) | A1ft | ft M1A0M1 if their first expansion has at least 3 terms after simplification |
| Alternative method 2 | ||
| \(2x^2 + 3xy - 8x - 12y\) | M1 | oe Allow one error eg \(\;2x^2 + 3xy - 8x + 12y\) |
| \(2x^2 + 3xy - 8x - 12y\) | A1 | oe Fully correct |
| \(4x^3 + 6x^2y - 16x^2 - 24xy\) or \((+)\ 6x^2y + 9xy^2 - 24xy - 36y^2\) | M1dep | oe ft correct multiplication of their expansion by \(2x\) or by \(3y\) if their expansion for first M1 has at least 3 terms after simplification |
| \(4x^3 + 12x^2y + 9xy^2 - 16x^2 - 48xy - 36y^2\) | A1ft | ft M1A0M1 if their first expansion has at least 3 terms after simplification |
Additional guidance
| Terms and variables may be in any order for M and A marks | |
| For M1 A1 M1dep terms may be seen in a grid | |
| \(4x^3 - 16x^2 + 9xy^2 - 36y^2\) from \((x - 4)(4x^2 + 9y^2)\) | M0A0M0A0 |
| In alt 2, condone \((2x^2 + 3xy - 8x - 12y)^2\) for M1A1 only | |
| One error can be one incorrect term or a missing or extra term | |
| Do not ignore fw when awarding the final A mark | |
| If \((x - 4)(2x + 3y)\) and \((2x + 3y)^2\) are both attempted and no answer is given, mark both and award the better mark |