According to the Distributive Property, which is a way to rewrite the algebraic expression (3x-1)(x-4)
3x^2+6x+4
3x^2-5x+4
3x(x)+3x(-4)+-1(x)+-1(-4)
3x(-1)+3x(3x)+x(-4)+x(x)
The correct way to rewrite the expression (3x-1)(x-4) using the Distributive Property is:
3x(x) + 3x(-4) + (-1)(x) + (-1)(-4)
This simplifies to:
3x^2 - 12x - x + 4
Combining like terms:
3x^2 - 13x + 4
Use the Distributive Property to find which expression is equivalent to 9x^2-25
9x(x-25)
(3x+5)(3x-5)
(3x+5)^2
(4.5x+12.5)(4.5x-12.5)
To rewrite the expression 9x^2 - 25 using the Distributive Property, we need to find an expression that factors the given expression into two terms.
The expression equivalent to 9x^2 - 25 using the Distributive Property is (3x+5)(3x-5).
Use the Distributive Property to verify which expression is equivalent to (x-5)(x-3)
x^2-2x+15
x^2-8x+15
3x^2-4x^2-3x-15
2x-2
To verify which expression is equivalent to (x-5)(x-3) using the Distributive Property, we can expand the given expression by multiplying each term from the first factor (x-5) by each term from the second factor (x-3).
(x-5)(x-3) = x(x) + x(-3) + (-5)(x) + (-5)(-3)
= x^2 - 3x - 5x + 15
= x^2 - 8x + 15
Therefore, the expression equivalent to (x-5)(x-3) using the Distributive Property is x^2 - 8x + 15.
Which expression is equivalent to (z+4)(z-4)
z^2+4z-4z-16
z^2-8z-16
z(z)+4z(z)-4(4)
2z^2-z^2-8
The expression equivalent to (z+4)(z-4) using the Distributive Property is:
(z+4)(z-4) = z(z) + z(-4) + 4(z) + 4(-4)
= z^2 - 4z + 4z - 16
= z^2 - 16
Therefore, the expression equivalent to (z+4)(z-4) is z^2 - 16.
What is another way to write the expression 2(x+1)(x+2)
2x^2+5x+2
x^2+6x+2
2x^2+3x+2
2x^2+6x+4
Another way to write the expression 2(x+1)(x+2) is:
2x(x) + 2x(2) + 1(x) + 1(2)
This simplifies to:
2x^2 + 4x + x + 2
Combining like terms:
2x^2 + 5x + 2
Therefore, the correct expression is 2x^2 + 5x + 2.
To determine the correct answer according to the Distributive Property, you need to distribute each term in the first parenthesis to every term in the second parenthesis.
Let's break it down step by step using the expression (3x-1)(x-4):
Step 1: Distribute the first term 3x in the first parenthesis to both terms in the second parenthesis:
(3x * x) + (3x * -4)
This results in 3x^2 -12x.
Step 2: Distribute the second term -1 in the first parenthesis to both terms in the second parenthesis:
(-1 * x) + (-1 * -4)
This results in -x + 4.
Finally, combine the results from Step 1 and Step 2 to get the simplified expression:
3x^2 - 12x - x + 4
Combine like terms:
3x^2 - 13x + 4
Therefore, the correct way to rewrite the expression (3x-1)(x-4) using the Distributive Property is: 3x^2 - 13x + 4.