Can I have an example of using the distributive property for a negative monomial times a trinomial with different signs on the terms and, showing each step of the distribution?
-dx * (ax^2 - bx + c)
= -adx^3 + bdx^2 -cdx
Thanks so much!
Certainly! Let's use the distributive property to multiply a negative monomial by a trinomial.
Suppose we have the expression: -2x(3x - 4 + 5x).
To apply the distributive property, we will distribute the -2x to each term inside the parentheses.
Step 1: Multiply the negative monomial (-2x) by the first term inside the parentheses (3x):
(-2x) * (3x) = -6x^2
Step 2: Multiply the negative monomial (-2x) by the second term inside the parentheses (-4):
(-2x) * (-4) = 8x
Step 3: Multiply the negative monomial (-2x) by the third term inside the parentheses (5x):
(-2x) * (5x) = -10x^2
After distributing -2x to each term, the expression becomes:
-6x^2 + 8x - 10x^2
Now, you can combine like terms:
-6x^2 - 10x^2 = -16x^2
8x remains the same.
Therefore, the final expression after distributing and combining like terms is:
-16x^2 + 8x