Question

Which of the following equations demonstrates the Associative Property?(1 point) Responses 3x⋅(4x⋅5)=3x(4x+5)3x⋅(4x⋅5)=3x(4x+5) 3 x times left parenthesis 4 x times 5 right parenthesis equals 3 x left parenthesis 4 x plus 5 right parenthesis 3x⋅(4x+5x)=(3x+4x)⋅53x⋅(4x+5x)=(3x+4x)⋅5 3 x times left parenthesis 4 x plus 5 x right parenthesis equals left parenthesis 3 x plus 4 x right parenthesis times 5 (3x+4x)⋅5=3x+(4x⋅5)(3x+4x)⋅5=3x+(4x⋅5) left parenthesis 3 x plus 4 x right parenthesis times 5 equals 3 x plus left parenthesis 4 x times 5 right parenthesis 3x⋅(4x⋅5)=(3x⋅4x)⋅5

Answer 1

The Associative Property states that the way in which numbers are grouped in addition or multiplication does not change the result. For multiplication, this means that \( (a \cdot b) \cdot c = a \cdot (b \cdot c) \).

Looking at the provided options, the equation that demonstrates the Associative Property is:

\( 3x \cdot (4x \cdot 5) = (3x \cdot 4x) \cdot 5 \)

This equation shows that the grouping of the factors does not affect the product, which is the essence of the Associative Property of multiplication.

Answer 2

Find the sum. (4p−2p2+8)+(5p2+2p)+(7−3p)(4p−2p2+8)+(5p2+2p)+(7−3p) (1 point) Responses 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+15−2p2+8p+15 negative 2 p squared plus 8 p plus 15 3p2+6p+153p2+6p+15

Answer 3

To find the sum \((4p - 2p^2 + 8) + (5p^2 + 2p) + (7 - 3p)\), let's first group the like terms together.

1. Identify and combine constant terms:

   • Constants: \(8 + 7 = 15\)

2. Identify and combine \(p\) terms:

   • \(p\) terms: \(4p + 2p - 3p = 3p\)

3. Identify and combine \(p^2\) terms:

   • \(p^2\) terms: \(-2p^2 + 5p^2 = 3p^2\)

Now, we can combine everything together:

\[ 3p^2 + 3p + 15 \]

So, the correct answer is:

3p² + 3p + 15.