(x%2B3).jpeg "(x^2-4x+4)(x+3)")
Expanding and Simplifying the Expression (x^2 - 4x + 4)(x + 3)
This expression involves multiplying two polynomials. To simplify it, we can use the distributive property (also known as FOIL method).
Step 1: Distribute the first polynomial over the second
We begin by multiplying each term in the first polynomial (x² - 4x + 4) with each term in the second polynomial (x + 3):
(x^2 - 4x + 4)(x + 3) = x^2(x + 3) - 4x(x + 3) + 4(x + 3)
Step 2: Apply the distributive property to each term
Now, we distribute each term in the first polynomial:
x^2(x + 3) = x^3 + 3x^2
-4x(x + 3) = -4x^2 - 12x
4(x + 3) = 4x + 12
Step 3: Combine like terms
Finally, we combine the terms with the same powers of x:
x^3 + 3x^2 - 4x^2 - 12x + 4x + 12 = **x^3 - x^2 - 8x + 12**
Conclusion
Therefore, the expanded and simplified form of the expression (x^2 - 4x + 4)(x + 3) is x³ - x² - 8x + 12.