Question

1)3a²-3b² 2) 6x²-24 3)x³-9x

Answer 1

$\displaystyle \tt 1) \: 3a^2-3b^2=3(a^2-b^2)=3(a-b)(a+b)\\2) \: 6x^2-24=6(x^2-4)=6(x-2)(x+2)\\3) \: x^3-9x=x(x^2-9)=x(x-3)(x+3)$

Answer 2

1. The expression 3a² - 3b² can be factored using the difference of squares formula. The formula states that a² - b² = (a + b)(a - b). Applying this formula to the given expression, we have:

3a² - 3b² = 3(a² - b²) = 3(a + b)(a - b)

So the factored form of 3a² - 3b² is 3(a + b)(a - b).

2. The expression 6x² - 24 can be factored by finding the greatest common factor (GCF) of the terms. In this case, the GCF is 6:

6x² - 24 = 6(x² - 4)

Now, we can use the difference of squares formula again to factor the quadratic term:

6(x² - 4) = 6(x + 2)(x - 2)

Therefore, the factored form of 6x² - 24 is 6(x + 2)(x - 2).

3. The expression x³ - 9x can be factored by factoring out the greatest common factor (GCF), which in this case is x:

x³ - 9x = x(x² - 9)

The quadratic term x² - 9 is a difference of squares and can be factored as follows:

x(x² - 9) = x(x + 3)(x - 3)

So the factored form of x³ - 9x is x(x + 3)(x - 3).