(x%2B1)(x%2B2).jpeg "(4x-3)(x+1)(x+2)")
Expanding and Simplifying (4x-3)(x+1)(x+2)
This article will guide you through the process of expanding and simplifying the expression (4x-3)(x+1)(x+2).
Step 1: Expanding the First Two Factors
We start by expanding the first two factors, (4x-3)(x+1):
(4x-3)(x+1) = 4x(x+1) - 3(x+1)
Applying the distributive property:
= 4x^2 + 4x - 3x - 3
Combining like terms:
= 4x^2 + x - 3
Step 2: Expanding the Result with the Third Factor
Now, we multiply the result from Step 1, (4x^2 + x - 3), by the third factor, (x+2):
(4x^2 + x - 3)(x+2) = 4x^2(x+2) + x(x+2) - 3(x+2)
Applying the distributive property again:
= 4x^3 + 8x^2 + x^2 + 2x - 3x - 6
Step 3: Combining Like Terms
Finally, we combine the like terms to obtain the simplified expression:
= **4x^3 + 9x^2 - x - 6**
Therefore, the expanded and simplified form of (4x-3)(x+1)(x+2) is 4x^3 + 9x^2 - x - 6.