Multiply a sum by a difference, step by step
(x + 8)(x − 8) is a sum times a difference, so the answer is x² − 64 with no middle term to work out.
The question
(x + 10)(x − 10) − 10
(x + 10)(x − 10)=x² − 100
x² − 100 − 10
−100 − 10 = −110
(x + 10)(x − 10) − 10=x² − 110
- The two brackets hold the same two things — x and 10 — with a + in one and a − in the other. That is a sum times a difference, so the product is the difference of their squares: no middle term to work out.
- 10 squared is 100, so the brackets come to x² − 100. Now the 10 that was waiting outside them: −100 − 10 is −110.
- So (x + 10)(x − 10) − 10 is x² − 110: the brackets multiply to x² − 100, and −100 − 10 is −110.
How it works.
- 01
The two brackets hold the same two things — x and 10 — with a + in one and a − in the other. That is a sum times a difference, so the product is the difference of their squares: no middle term to work out.
- 02
10 squared is 100, so the brackets come to x² − 100. Now the 10 that was waiting outside them: −100 − 10 is −110.
- 03
So (x + 10)(x − 10) − 10 is x² − 110: the brackets multiply to x² − 100, and −100 − 10 is −110.