Use the Distributive Property to rewrite the polynomial (x+8)(x−2).

Answer 1

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.

Answer 2

Find the product of the polynomials (2x+1)(x−4)
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Answer 3

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.

Answer 4

According to the Distributive Property, which is a way to rewrite the algebraic expression (3x−1)(x−4)?

Answer 5

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.

Answer 6

Use the Distributive Property to find which expression is equivalent to 9x2−25.

Answer 7

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).

Answer 8

Which expression is equivalent to (z+4)(z−4)

Answer 9

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.

Answer 10

Use the Distributive Property to verify which expression is equivalent to (x−5)(x−3)

Answer 11

To verify which expression is equivalent to (x−5)(x−3) using the Distributive Property, we need to distribute each term of the first expression to each term of the second expression.

First, distribute the x term of the first expression to each term of the second expression:

x * x = x^2
x * (-3) = -3x

Next, distribute the -5 term of the first expression to each term of the second expression:

-5 * x = -5x
-5 * (-3) = 15

Now, we can combine the like terms:

(x−5)(x−3) = x^2 - 3x - 5x + 15

Simplifying further:

(x−5)(x−3) = x^2 - 8x + 15

Therefore, the expression equivalent to (x−5)(x−3) is x^2 - 8x + 15.