am i correct?
1(2x)^3 + 3(2x)^2*(-5y)^1 + 3(2x)^1*(-5y)^2 + 1(-5y)^3
answer
(2x-5y)^3
Anything times 1 or to the first power is itself. Unless you have typos, here is what I get:
(2x)^3 + 12x^2 * (-5y) + 6x * 25y^2 - 125y^3 =
8x^3 - 60x^2y + 150xy^2 - 125y^3
luckily, the answers agree!
Ok,thank you guys! :)
To determine if your answer is correct, we can simplify the expression using the binomial expansion formula:
(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
Let's apply this formula to the given expression step by step:
1(2x)^3 + 3(2x)^2*(-5y)^1 + 3(2x)^1*(-5y)^2 + 1(-5y)^3
= (8x^3) + 3(4x^2)(-5y) + 3(2x)(25y^2) + (-125y^3)
= 8x^3 - 60x^2y + 150xy^2 - 125y^3
Now, let's compare this simplified expression with your answer, (2x - 5y)^3.
(2x - 5y)^3 = (2x - 5y)(2x - 5y)(2x - 5y)
Expanding this using the distributive property gives us:
= (4x^2 - 20xy + 25y^2)(2x - 5y)
= 8x^3 - 40x^2y + 50xy^2 - 20x^2y + 100xy^2 - 125y^3
= 8x^3 - 60x^2y + 150xy^2 - 125y^3
As we can see, your answer (2x - 5y)^3 matches the simplified form of the given expression. Therefore, your answer is correct.