According to the Distributive Property, which is a way to rewrite the algebraic expression (3x -1)(x-4)
To rewrite the algebraic expression (3x -1)(x-4) using the Distributive Property, we distribute each term of the first expression (3x - 1) to each term of the second expression (x - 4):
(3x - 1)(x - 4) = 3x(x) + 3x(-4) - 1(x) - 1(-4)
This simplifies to:
= 3x^2 - 12x - x + 4
= 3x^2 - 13x + 4
To rewrite the algebraic expression (3x - 1)(x - 4) using the Distributive Property, you need to multiply each term in the first parenthesis with each term in the second parenthesis.
Here are the steps:
1. Multiply the first term of the first parenthesis (3x) by each term in the second parenthesis:
3x * x = 3x^2
3x * -4 = -12x
2. Multiply the second term of the first parenthesis (-1) by each term in the second parenthesis:
-1 * x = -x
-1 * -4 = 4
3. Combine the like terms:
3x^2 - 12x - x + 4
4. Simplify the expression:
3x^2 - 13x + 4
Therefore, using the Distributive Property, the expression (3x - 1)(x - 4) can be rewritten as 3x^2 - 13x + 4.
To rewrite the algebraic expression (3x - 1)(x - 4) using the Distributive Property, you need to multiply each term from the first expression (3x - 1) by each term from the second expression (x - 4). This can be done by using the FOIL method. Here's how:
Step 1: Start by multiplying the first terms of each expression. In this case, it is 3x * x, which gives you 3x^2.
Step 2: Next, multiply the outer terms, which are 3x * -4. This gives you -12x.
Step 3: Proceed to multiply the inner terms, which are -1 * x. This gives you -x.
Step 4: Finally, multiply the last terms, -1 * -4, which gives you 4.
Step 5: Collect and combine the like terms. In this case, the like terms are -12x and -x. Adding them together gives you -13x.
Putting it all together, the rewritten algebraic expression using the Distributive Property is: 3x^2 - 13x + 4.