According to the Distributive Property, which expression is equivalent to 4x3+8x2+12x
?
The expression that is equivalent to 4x3+8x2+12x, according to the distributive property, is 4(x^3) + 8(x^2) + 12(x).
According to the Distributive Property, which expression is equivalent to 4x3+8x2+12x
?(
A. (2x2+4)(2x−3)
B. 4x(4x+5x)
C. (2x2+4)(2x2+3)
D. 4x(x2+2x+3)
The correct answer is D. 4x(x²+2x+3).
To find an expression equivalent to 4x3+8x2+12x using the Distributive Property, we need to factor out the common factor from each term.
Step 1: Find the greatest common factor (GCF) of the coefficients, which are 4, 8, and 12. The GCF of 4, 8, and 12 is 4.
Step 2: Factor out the GCF from each term:
4x3 = 4 * x^3 = 4x * x^2
8x2 = 4 * 2 * x^2 = 4x * 2x
12x = 4 * 3 * x = 4x * 3
Step 3: Combine the factored terms:
4x3+8x2+12x = (4x * x^2) + (4x * 2x) + (4x * 3)
Step 4: Apply the Distributive Property:
= 4x(x^2) + 4x(2x) + 4x(3)
Step 5: Simplify:
= 4x^3 + 8x^2 + 12x
Therefore, the expression 4x(x^2) + 4x(2x) + 4x(3) is equivalent to 4x3+8x2+12x according to the Distributive Property.
To use the Distributive Property, we distribute the number or variable outside the parentheses to each term inside the parentheses.
In this case, we have the expression 4x(3+8+12x).
To simplify this expression, we multiply 4x by each term inside the parentheses:
4x * 3 = 12x
4x * 8 = 32x
4x * 12x = 48x^2
Now we add these terms together:
12x + 32x + 48x^2
This gives us the equivalent expression to 4x(3+8+12x): 48x^2 + 44x.