Adding and subtracting polynomials, step by step
Adding polynomials is collecting like terms with more kinds of term to collect.
The question
Write the answer as a polynomial.
(x + 9)(x + 1)
(x + 9)(x + 1)
x²+x
+9x+9
x + 9x = 10x
=x² + 10x + 9
- Two brackets means every term in the first has to meet every term in the second — two times two is FOUR multiplications, not two. Miss one and the x term comes out short.
- x × x = x², and x × 1 = x.
- Then the other one: 9 × x = 9x, and 9 × 1 = 9.
- Two of those four are x terms, so they collect: x + 9x = 10x. The answer is x² + 10x + 9.
How it works.
- 01
Two brackets means every term in the first has to meet every term in the second — two times two is FOUR multiplications, not two. Miss one and the x term comes out short.
- 02
x × x = x², and x × 1 = x.
- 03
Then the other one: 9 × x = 9x, and 9 × 1 = 9.
- 04
Two of those four are x terms, so they collect: x + 9x = 10x. The answer is x² + 10x + 9.