To expand (x + 3)(x + 5), multiply every term in the first bracket by every term in the second. That gives four products: x × x = x², x × 5 = 5x, 3 × x = 3x and 3 × 5 = 15. Collect like terms: x² + 8x + 15.
A grid helps you keep track: write one bracket along the top and the other down the side, fill in the products and add them. Watch the signs: (x + 4)(x − 4) = x² − 4x + 4x − 16 = x² − 16. This is the difference of two squares.
Worked example
Expand and simplify (2x − 3)(x + 5)
- 2x × x = 2x², 2x × 5 = 10x, −3 × x = −3x, −3 × 5 = −15.
- Collect: 10x − 3x = 7x.
Answer:2x² + 7x − 15
Key words
- expand
- multiply out the brackets
- like terms
- terms with the same letters and powers
- difference of two squares
- (a + b)(a − b) = a² − b²
Practise this
New questions every time.
Common Core-referenced: HSA-APR.A.1