Question

(x+2)•(x-2) (3a-5b)•(5b+3a) (3a+b)² (3x²-5y)² (x-3)²-x²

Answer 1

(x+2)(x-2)= x²-4

(3a-5b)(5b+3a)= 9a²-25b²

(3a+b)²= 9a²+6ab+b²

(3x²-5y)²=9x⁴-30x²y+25y²

(x-3)²-x²= (x-3-x)(x-3+x)= -3*(2x-3)

Answer 2

Let's simplify each of the expressions:

1. (x + 2) • (x - 2) Expanding this expression using the distributive property, we get: (x + 2) • (x - 2) = x • (x - 2) + 2 • (x - 2) = x² - 2x + 2x - 4 = x² - 4

2. (3a - 5b) • (5b + 3a) Using the distributive property, we have: (3a - 5b) • (5b + 3a) = 3a • (5b + 3a) - 5b • (5b + 3a) = 15ab + 9a² - 25b² - 15ab = 9a² - 25b²

3. (3a + b)² Expanding using the square of a binomial formula, we get: (3a + b)² = (3a)² + 2(3a)(b) + (b)² = 9a² + 6ab + b²

4. (3x² - 5y)² Expanding using the square of a binomial formula, we have: (3x² - 5y)² = (3x²)² - 2(3x²)(5y) + (5y)² = 9x⁴ - 30x²y + 25y²

5. (x - 3)² - x² Expanding and simplifying, we have: (x - 3)² - x² = (x)² - 2(x)(3) + (3)² - x² = x² - 6x + 9 - x² = -6x + 9

Therefore, the simplified expressions are:

1. (x + 2) • (x - 2) = x² - 4
2. (3a - 5b) • (5b + 3a) = 9a² - 25b²
3. (3a + b)² = 9a² + 6ab + b²
4. (3x² - 5y)² = 9x⁴ - 30x²y + 25y²
5. (x - 3)² - x² = -6x + 9