Use the Distributive Property to rewrite the expression (3x−5)(2x+2)

Question

.(1 point)
Responses

6x2−3x−10
6 x squared minus 3 x minus 10

5x2−2x−3
5 x squared minus 2 x minus 3

x2−3x−10
x squared minus 3 x minus 10

6x2−4x−10

Answer 1

To use the Distributive Property to rewrite the expression \((3x−5)(2x+2)\), we need to multiply each term in the first parentheses by each term in the second parentheses.

Let's perform the multiplication step by step:

1. Multiply \(3x\) by \(2x\): \[ 3x \cdot 2x = 6x^2 \]

2. Multiply \(3x\) by \(2\): \[ 3x \cdot 2 = 6x \]

3. Multiply \(-5\) by \(2x\): \[ -5 \cdot 2x = -10x \]

4. Multiply \(-5\) by \(2\): \[ -5 \cdot 2 = -10 \]

Now, combine all the results: \[ 6x^2 + 6x - 10x - 10 \]

Combine like terms (\(6x - 10x\)): \[ 6x^2 - 4x - 10 \]

Thus, the expression \((3x−5)(2x+2)\) rewritten using the Distributive Property is: \[ 6x^2 - 4x - 10 \]

The correct response is: 6x²−4x−10.

Answer 2

Use the Distributive Property to write the expression 4x2−36
a different way.(1 point)
Responses

(2x+9)(x−9)
left parenthesis 2 x plus 9 right parenthesis left parenthesis x minus 9 right parenthesis

4x(x−9)
4 x left parenthesis x minus 9 right parenthesis

(x+18)(x−18)
left parenthesis x plus 18 right parenthesis left parenthesis x minus 18 right parenthesis

(2x+6)(2x−6)

Answer 3

To use the Distributive Property to rewrite the expression \(4x^2 - 36\) in a different way, we can first recognize that this expression is a difference of squares.

Notice that: \[ 4x^2 - 36 = (2x)^2 - 6^2 \]

We can use the difference of squares formula, which states that \(a^2 - b^2 = (a + b)(a - b)\).

In this case, \(a = 2x\) and \(b = 6\). So we apply the formula: \[ (2x + 6)(2x - 6) \]

Now we can check the options given:

1. \((2x+9)(x−9)\)
2. \(4x(x−9)\)
3. \((x+18)(x−18)\)
4. \((2x+6)(2x−6)\)

The correct response here is: (2x + 6)(2x - 6).