According to the Distributive Property, which is a way to rewrite the algebraic expression (3x−1)(x−4)?
According to the Distributive Property, the expression (3x-1)(x-4) can be rewritten as 3x(x) + 3x(-4) + (-1)(x) + (-1)(-4).
The distributive property states that for any three numbers a, b, and c, the product of a and the sum of b and c is equal to the sum of the products of a and b and a and c.
To rewrite the algebraic expression (3x−1)(x−4) using the distributive property, we can distribute the 3x to both terms inside the parentheses (x and -4) and then distribute the -1 to both terms inside the parentheses as well.
Here are the steps:
1. Distribute the 3x to both terms inside the parentheses:
(3x)(x) + (3x)(-4)
2. Distribute the -1 to both terms inside the parentheses:
(-1)(x) + (-1)(-4)
3. Simplify each multiplication:
3x^2 - 12x - x + 4
4. Combine like terms:
3x^2 - 13x + 4
Therefore, by using the distributive property, we have rewritten the original expression (3x−1)(x−4) as 3x^2 - 13x + 4.