Factor these:
8x^3-125
81x^-625
18x^3+63x^2-50x-175
x^4-11x^2+18
I'm so lost!
differece of cubes
differece of cubes
9x^2(2x+7)-25(2x+7) then gather the common factor, to (2x+7)(9x^2-25), and now the second term is a differece of squares, so It can be factored.
Last
(x^2-9)(x^2-2) both of these terms are difference of squares. (last term (x-sqrt2)(x+sqrt2)
No worries! I'm here to help you understand how to factor these expressions.
1. To factor the expression 8x^3 - 125, we can use the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). In this case, a = 2x and b = 5. So we have:
8x^3 - 125 = (2x - 5)(4x^2 + 10x + 25).
2. The expression 81x^2 - 625 is not a factorable expression, but it is recognizable as the difference of squares. The formula for the difference of squares is a^2 - b^2 = (a + b)(a - b). In this case, a = 9x and b = 25. So we have:
81x^2 - 625 = (9x + 25)(9x - 25).
3. To factor the expression 18x^3 + 63x^2 - 50x - 175, we can use factor by grouping. First, let's group the terms with a common factor:
(18x^3 + 63x^2) - (50x + 175).
Next, factor out the common factors from each group:
9x^2(2x + 7) - 25(2x + 7).
Notice that we now have a common binomial factor, (2x + 7). We can factor that out:
(2x + 7)(9x^2 - 25).
4. The expression x^4 - 11x^2 + 18 can be factored using factoring by grouping as well. Let's rewrite the expression as:
(x^4 - 9x^2) - (2x^2 - 18).
We now have two groups which can be factored separately:
x^2(x^2 - 9) - 2(x^2 - 9).
Again, we have a common binomial factor, (x^2 - 9), which we can factor out:
(x^2 - 9)(x^2 - 2).
I hope this helps you understand how to factor these expressions!