Use the Distributive Property to rewrite the polynomial (x+8)(x−2).
To rewrite the polynomial (x+8)(x−2) using the distributive property, we need to distribute each term of the first polynomial (x+8) to each term of the second polynomial (x−2).
First, distribute the x term of the first polynomial to each term of the second polynomial:
x * x = x^2
x * (-2) = -2x
Next, distribute the 8 term of the first polynomial to each term of the second polynomial:
8 * x = 8x
8 * (-2) = -16
Now, we can combine the like terms:
(x+8)(x−2) = x^2 - 2x + 8x - 16
Simplifying further:
(x+8)(x−2) = x^2 + (8x - 2x) - 16
(x+8)(x−2) = x^2 + 6x - 16
Therefore, the polynomial (x+8)(x−2) can be rewritten as x^2 + 6x - 16.
Find the product of the polynomials (2x+1)(x−4)
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To find the product of the polynomials (2x+1)(x−4), we will use the distributive property.
First, distribute the 2x term of the first polynomial to each term of the second polynomial:
2x * x = 2x^2
2x * (-4) = -8x
Next, distribute the 1 term of the first polynomial to each term of the second polynomial:
1 * x = x
1 * (-4) = -4
Now, we can combine the like terms:
(2x+1)(x−4) = 2x^2 - 8x + x - 4
Simplifying further:
(2x+1)(x−4) = 2x^2 - 7x - 4
Therefore, the product of the polynomials (2x+1)(x−4) is 2x^2 - 7x - 4.
According to the Distributive Property, which is a way to rewrite the algebraic expression (3x−1)(x−4)?
According to the distributive property, we can rewrite the algebraic expression (3x−1)(x−4) by distributing each term of the first expression to each term of the second expression.
First, distribute the 3x term of the first expression to each term of the second expression:
3x * x = 3x^2
3x * (-4) = -12x
Next, distribute the -1 term of the first expression to each term of the second expression:
-1 * x = -x
-1 * (-4) = 4
Now, we can combine the like terms:
(3x−1)(x−4) = 3x^2 - 12x - x + 4
Simplifying further:
(3x−1)(x−4) = 3x^2 - 13x + 4
Therefore, according to the distributive property, the expression (3x−1)(x−4) can be rewritten as 3x^2 - 13x + 4.
Use the Distributive Property to find which expression is equivalent to 9x2−25.
To use the Distributive Property to find an equivalent expression to 9x^2 - 25, we need to identify two binomials whose product gives us that expression.
First, let's look at the expression 9x^2 - 25. Notice that this can be written as a difference of squares: (3x)^2 - 5^2.
Using the formula for the difference of squares, we can rewrite 9x^2 - 25 as:
(3x - 5)(3x + 5)
So, the binomial expression that is equivalent to 9x^2 - 25, using the Distributive Property, is (3x - 5)(3x + 5).
Which expression is equivalent to (z+4)(z−4)
The expression (z+4)(z−4) can be simplified using the distributive property.
First, distribute the z term of the first expression to each term of the second expression:
z * z = z^2
z * (-4) = -4z
Next, distribute the 4 term of the first expression to each term of the second expression:
4 * z = 4z
4 * (-4) = -16
Now, we can combine the like terms:
(z+4)(z−4) = z^2 - 4z + 4z - 16
Simplifying further:
(z+4)(z−4) = z^2 - 16
Therefore, the expression equivalent to (z+4)(z−4) is z^2 - 16.