Factor: 27-(m+2n)^3
I've tried it but my answer was incorrect.
recall that a^3-b^3 = (a-b)(a^2+ab+b^2)
You have
3^3 - (m+2n)^3
= (3-(m+2n))(3^2 + 3(m+2n) + (m+2n)^2)
= (3-m-2n)(9+3m+6n+m^2+4mn+4n^2)
I think I like the original way more . . .
To factor the expression 27 - (m + 2n)^3, let's break it down step by step:
Step 1: Recognize the pattern
Notice that the given expression follows the pattern for the difference of cubes: a^3 - b^3. In this case, a = 3 and b = (m + 2n).
Step 2: Apply the formula for the difference of cubes
The formula for the difference of cubes is:
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
Step 3: Substitute the values
Replace a with 3 and b with (m + 2n) in the formula:
(3 - (m + 2n))(3^2 + 3(m + 2n) + (m + 2n)^2)
Step 4: Simplify
Simplify the expression:
(3 - (m + 2n))(9 + 3m + 6n + m^2 + 4mn + 4n^2)
Now, you can distribute (3 - (m + 2n)) to each term inside the parentheses to complete the factoring process.