(x%5E2-4x%2B16).jpeg "(x+4)(x^2-4x+16)")
Expanding the Expression (x+4)(x^2-4x+16)
This expression represents the multiplication of a binomial and a trinomial. We can use the distributive property (or FOIL method) to expand this expression.
Understanding the Terms
- (x + 4) is a binomial, meaning it has two terms.
- (x² - 4x + 16) is a trinomial, meaning it has three terms.
Applying the Distributive Property
We distribute each term of the binomial (x + 4) to every term of the trinomial (x² - 4x + 16).
-
x * (x² - 4x + 16):
- x * x² = x³
- x * -4x = -4x²
- x * 16 = 16x
-
4 * (x² - 4x + 16):
- 4 * x² = 4x²
- 4 * -4x = -16x
- 4 * 16 = 64
Combining Like Terms
Now we combine all the terms:
x³ - 4x² + 16x + 4x² - 16x + 64
Notice that the -4x² and 4x² terms cancel out, and the 16x and -16x terms also cancel out.
The Final Result
Therefore, the expanded form of (x + 4)(x² - 4x + 16) is:
x³ + 64
This result showcases a special case where the expanded form simplifies to a binomial due to the cancellation of terms. This pattern is directly related to the sum of cubes factorization.