Use the Distributive Property to rewrite the expression (3x−5)(2x+2)(3x−5)(2x+2) .(1 point) Responses x2−3x−10x2−3x−10 x squared minus 3 x minus 10 5x2−2x−35x2−2x−3 5 x squared minus 2 x minus 3 6x2−3x−106x2−3x−10 6 x squared minus 3 x minus 10 6x2−4x−10

Answer 1

To rewrite the expression \((3x-5)(2x+2)(3x-5)(2x+2)\) using the Distributive Property, we first simplify it step by step.

1. Start by recognizing that we can rewrite this as \((3x-5)(2x+2)\) squared, i.e., \(\left((3x-5)(2x+2)\right)^2\).

2. Now, let's focus on simplifying \((3x-5)(2x+2)\) using the distributive property (also known as the FOIL method for binomials): \[ (3x-5)(2x+2) = 3x \cdot 2x + 3x \cdot 2 - 5 \cdot 2x - 5 \cdot 2 \]

   Calculating each term:

   • \(3x \cdot 2x = 6x^2\)
   • \(3x \cdot 2 = 6x\)
   • \(-5 \cdot 2x = -10x\)
   • \(-5 \cdot 2 = -10\)

   Putting it all together: \[ 6x^2 + 6x - 10x - 10 = 6x^2 - 4x - 10 \]

3. Now we need to square this result: \[ (6x^2 - 4x - 10)^2 \]

   However, since the question asks for rewriting the original product (not necessarily expanding), the simplified version before squaring is sufficient.

Thus, the simplified expression is: \[ \boxed{6x^2 - 4x - 10} \]

Answer 2

Find the expression that is equivalent to 3x2+2x−5x−2x2+23x2+2x−5x−2x2+2 .(1 point) Responses (x+1)(x+2)(x+1)(x+2) left parenthesis x plus 1 right parenthesis left parenthesis x plus 2 right parenthesis (x+2)(x−2)(x+2)(x−2) left parenthesis x plus 2 right parenthesis left parenthesis x minus 2 right parenthesis (3x+2)(x+1)(3x+2)(x+1) left parenthesis 3 x plus 2 right parenthesis left parenthesis x plus 1 right parenthesis (x−2)(x−1)

Answer 3

To simplify the expression \(3x^2 + 2x - 5x - 2x^2 + 2\), we'll start by combining like terms.

1. Combine the \(x^2\) terms:

   • \(3x^2 - 2x^2 = x^2\)

2. Combine the \(x\) terms:

   • \(2x - 5x = -3x\)

3. The constant term remains:

   • \(+2\)

Now, putting it all together, we have: \[ x^2 - 3x + 2 \]

Next, we can factor this quadratic expression. We are looking for two numbers that multiply to \(+2\) (the constant term) and add up to \(-3\) (the linear coefficient).

The numbers that satisfy these conditions are \(-2\) and \(-1\). Therefore, we can factor the quadratic as follows: \[ x^2 - 3x + 2 = (x - 2)(x - 1) \]

Therefore, the expression that is equivalent to \(3x^2 + 2x - 5x - 2x^2 + 2\) is: \[ \boxed{(x - 2)(x - 1)} \]

Answer 4

find the sum. (4p−2p2+8)+(5p2+2p)+(7−3p)(4p−2p2+8)+(5p2+2p)+(7−3p) (1 point) responses 3p2+6p+153p2+6p+15 3 p squared plus 6 p plus 15 5p2+p+155p2+p+15 5 p squared plus p plus 15 3p2+3p+153p2+3p+15 3 p squared plus 3 p plus 15 −2p2+8p+15

Answer 5

To find the sum of the expression \((4p - 2p^2 + 8) + (5p^2 + 2p) + (7 - 3p)\), we will start by combining the like terms.

1. Identify and separate the coefficients for \(p^2\), \(p\), and constant terms:

   • For \(p^2\): \(-2p^2 + 5p^2 = 3p^2\)
   • For \(p\): \(4p + 2p - 3p = 3p\)
   • For constant terms: \(8 + 7 = 15\)

2. Now, combine these results: \[ 3p^2 + 3p + 15 \]

Thus, the sum is: \[ \boxed{3p^2 + 3p + 15} \]