Answer:
9. (x + 10)² = x² + 20x + 100
10. (x - 10)² = x² - 20x + 100
Step-by-step explanation:
(x + 10)² is equivalent to:
(x + 10)² = (x + 10)(x + 10)
Now, we need to multiply the polynomials, so we will multiply each term of the first polynomial by each term of the second polynomial. Then:
(x + 10)² = x(x) + x(10) + 10(x) + 10(10)
(x + 10)² = x² + 10x + 10x + 100
(x + 10)² = x² + 20x + 100
In the same way, we can find the equivalent expression for (x - 10)², so:
(x - 10)² = (x - 10)(x - 10)
(x - 10)² = x(x) - x(10) - 10(x) + 10(10)
(x - 10)² = x² - 10x - 10x + 100
(x - 10)² = x² - 20x + 100
Therefore, the answers are:
(x + 10)² = x² + 20x + 100
(x - 10)² = x² - 20x + 100