Answers − Quadratic Expansion Foil Method
1. Expand (x + 4)(x + 2)
| First | ( | x | )( | x | ) = | + x2 | ||
| Outer | ( | x | )( | + 2 | ) = | + 2x | ||
| Inner | ( | + 4 | )( | x | ) = | + 4x | ||
| Last | ( | + 4 | )( | + 2 | ) = | + 8 |
= x2 + 2x + 4x + 8
= x2 + 6x + 8
2. Expand (x − 4)(x − 2)
| First | ( | x | )( | x | ) = | + x2 | ||
| Outer | ( | x | )( | − 2 | ) = | − 2x | ||
| Inner | ( | − 4 | )( | x | ) = | − 4x | ||
| Last | ( | − 4 | )( | − 2 | ) = | + 8 |
= x2 − 2x − 4x + 8
= x2 − 6x + 8
3. Expand (2x + 3)(x − 6)
| First | ( | 2x | )( | x | ) = | + 2x2 | ||
| Outer | ( | 2x | )( | − 6 | ) = | − 12x | ||
| Inner | ( | + 3 | )( | x | ) = | + 3x | ||
| Last | ( | + 3 | )( | − 6 | ) = | −18 |
= 2x2 − 12x + 3x − 18
= 2x2 − 9x − 18
4. Multiply out (2x − 3)(x + 6)
| First | ( | 2x | )( | x | ) = | + 2x2 | ||
| Outer | ( | 2x | )( | + 6 | ) = | + 12x | ||
| Inner | ( | − 3 | )( | x | ) = | −3x | ||
| Last | ( | − 3 | )( | + 6 | ) = | −18 |
= 2x2 + 12x − 3x − 18
= 2x2 + 9x − 18
5. Multiply out (x − 5)(3x + 3)
| First | ( | x | )( | 3x | ) = | + 3x2 | ||
| Outer | ( | x | )( | + 3 | ) = | + 3x | ||
| Inner | ( | − 5 | )( | 3x | ) = | −15x | ||
| Last | ( | − 5 | )( | + 3 | ) = | −15 |
= 3x2 + 3x − 15x − 15
= 3x2 − 12x − 15
6. Multiply out (x + 5)(3x − 3)
| First | ( | x | )( | 3x | ) = | + 3x2 | ||
| Outer | ( | x | )( | − 3 | ) = | − 3x | ||
| Inner | ( | + 5 | )( | 3x | ) = | + 15x | ||
| Last | ( | + 5 | )( | − 3 | ) = | −15 |
= 3x2 − 3x + 15x − 15
= 3x2 + 12x − 15
7. Remove the brackets (2x + 3)(4x + 3)
| First | ( | 2x | )( | 4x | ) = | + 8x2 | ||
| Outer | ( | 2x | )( | + 3 | ) = | + 6x | ||
| Inner | ( | + 3 | )( | 4x | ) = | + 12x | ||
| Last | ( | + 3 | )( | + 3 | ) = | + 9 |
= 8x2 + 6x + 12x + 9
= 8x2 + 18x + 9
8. Remove the brackets (2x − 3)(4x − 3)
| First | ( | 2x | )( | 4x | ) = | + 8x2 | ||
| Outer | ( | 2x | )( | − 3 | ) = | + 6x | ||
| Inner | ( | − 3 | )( | 4x | ) = | −12x | ||
| Last | ( | − 3 | )( | − 3 | ) = | + 9 |
= 8x2 − 6x − 12x + 9
= 8x2 − 18x + 9
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