According to the Distributive Property, which is a way to rewrite the algebraic expression (3x−1)(x−4)?(1 point)
Responses
3x2+6x+4
3 x squared plus 6 x plus 4
3x2−5x+4
3 x squared minus 5 x plus 4
3x(−1)+3x(3x)+x(−4)+x(x)
3 x left parenthesis negative 1 right parenthesis plus 3 x left parenthesis 3 x right parenthesis plus x left parenthesis negative 4 right parenthesis plus x left parenthesis x right parenthesis
3x(x)+3x(−4)+−1(x)+−1(−4)
3x(x) + 3x(-4) + -1(x) + -1(-4)
To rewrite the algebraic expression (3x−1)(x−4) using the distributive property, you will need to multiply each term in the first set of parentheses by each term in the second set of parentheses and then combine like terms.
First, multiply 3x by x and -1 by x:
3x * x = 3x^2
-1 * x = -x
Next, multiply 3x by -4 and -1 by -4:
3x * -4 = -12x
-1 * -4 = 4
Now, combine all the terms:
3x^2 - x - 12x + 4
Simplifying further, combine like terms:
3x^2 - 13x + 4
Thus, the expression (3x−1)(x−4) can be rewritten as 3x^2 - 13x + 4 using the distributive property.
To rewrite the algebraic expression (3x−1)(x−4) using the distributive property, you need to multiply each term from the first parentheses (3x and -1) with each term from the second parentheses (x and -4). This will give you four different multiplication terms. Let's break it down step by step:
1. Multiply 3x with x: 3x * x = 3x^2 (the product of the coefficients 3 and 1 is 3, and the exponent on the variable x is the sum of the exponents 1 + 1 = 2)
2. Multiply 3x with -4: 3x * -4 = -12x (the product of the coefficients 3 and -4 is -12, and the variable x remains as it is)
3. Multiply -1 with x: -1 * x = -x (the product of the coefficients -1 and 1 is -1, and the variable x remains as it is)
4. Multiply -1 with -4: -1 * -4 = 4 (the product of the coefficients -1 and -4 is 4)
Now, combine all the terms obtained in steps 1-4:
3x^2 - 12x - x + 4
Simplifying further, you can combine the -12x and -x terms:
3x^2 - 13x + 4
So, the rewritten algebraic expression using the distributive property is 3x^2 - 13x + 4.