Expand and simplify (x + 1)(x² − 4x + 5).(3 marks)
Draw a 2 × 3 grid.
| x² | −4x | +5 | ||
| x | ||||
| +1 |
In plain EnglishWrite the first bracket down the left side — x in the top row, +1 in the bottom row. Write the second bracket along the top — x², −4x, and +5 across the three columns.
Multiply each pair to fill every cell.
| x² | −4x | +5 | ||
| x | x³ | −4x² | +5x | ✓1 |
| +1 | +x² | −4x | +5 | ✓2 |
In plain EnglishWork through one cell at a time. Multiply the row label by the column label.
Row 1 (× x): x³, −4x², +5x
Row 2 (× 1): +x², −4x, +5
Row 1 (× x): x³, −4x², +5x
Row 2 (× 1): +x², −4x, +5
The circles on the grid show the like terms.
| x² | −4x | +5 | ||
| x | x³ | −4x² | +5x | ✓1 |
| +1 | +x² | −4x | +5 | ✓2 |
In plain EnglishBlue circles mark the x² terms: −4x² and +x².
Green circles mark the x terms: +5x and −4x.
The x³ and +5 have no matching terms.
Green circles mark the x terms: +5x and −4x.
The x³ and +5 have no matching terms.
Simplify each group and write the final answer.= x³ − 3x² + x + 5 ✓3
In plain Englishx² terms: −4x² + x² = −3x²
x terms: +5x − 4x = +x
x³ − 3x² + x + 5
x terms: +5x − 4x = +x
x³ − 3x² + x + 5
0 of 0 complete
Your turn
Type powers with ^, so x² is x^2 and x³ is x^3. Stuck? Tap Need a hint?
Past paper questions
Ready for exam-style questions? This collects every SQA past paper question on expanding brackets, with answers.
Expanding bracketsEvery National 5 expanding brackets question in one PDF, with answers.maths.scot · PDF Open ↗ (opens in a new tab)