Question

(a+5)(a-7)=?(3x-1)(2x+7)=?(a-1)(a²-2a-1)=?

Answer 1

1)a^2-2a-35. 2)6x^2+19x-7. 3)a^3-2a^2-a-a^2+2a+1=a^3-3a^2+a+1

Answer 2

Let's simplify each expression:

1. (a + 5)(a - 7) Expanding using the distributive property, we get: (a + 5)(a - 7) = a(a) + a(-7) + 5(a) + 5(-7) = a² - 7a + 5a - 35 = a² - 2a - 35

2. (3x - 1)(2x + 7) Using the distributive property: (3x - 1)(2x + 7) = (3x)(2x) + (3x)(7) + (-1)(2x) + (-1)(7) = 6x² + 21x - 2x - 7 = 6x² + 19x - 7

3. (a - 1)(a² - 2a - 1) Again, applying the distributive property: (a - 1)(a² - 2a - 1) = (a)(a²) + (a)(-2a) + (a)(-1) + (-1)(a²) + (-1)(-2a) + (-1)(-1) = a³ - 2a² - a - a² + 2a + 1 = a³ - 3a² + 1

Therefore: (a + 5)(a - 7) simplifies to a² - 2a - 35 (3x - 1)(2x + 7) simplifies to 6x² + 19x - 7 (a - 1)(a² - 2a - 1) simplifies to a³ - 3a² + 1