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.Using the Distributive Property to rewrite the expression (3x – 5)(2x + 2)

1 year ago

To rewrite the expression \((3x - 5)(2x + 2)\) using the Distributive Property, you need to distribute each term in the first parentheses by each term in the second parentheses. Here’s the step-by-step breakdown: 1. **Distribute \(3x\) to both terms in th...

1 year ago

To simplify \((3x - 5)(2x + 2)\), we can use the Distributive Property where we multiply each term in the first part by each term in the second part. Here’s how we do it step by step: 1. **First, we take \(3x\) and multiply it by both terms in the second...

1 year ago

Find the expression that is equivalent to 3𝑥2+2𝑥−5𝑥−2𝑥2+2 (𝑥−2)(𝑥−1) (𝑥+2)(𝑥−2) (𝑥+1)(𝑥+2)

1 year ago

To simplify the given expression \( \frac{3x^2 + 2x - 5x - 2x^2 + 2}{(x - 2)(x - 1)(x + 2)(x - 2)(x + 1)(x + 2)} \), we first need to simplify the numerator and the denominator. ### Step 1: Simplify the Numerator Start with the expression in the numerator...

1 year ago

Step 1: Simplify the Numerator First, let's focus on the top part, which is called the numerator: \[ 3x^2 + 2x - 5x - 2x^2 + 2 \] We can combine like terms here. Group the \(x^2\) terms together and the \(x\) terms together: \[ (3x^2 - 2x^2) + (2x - 5x) +...

1 year ago

To find the expression equivalent to \(\frac{3x^2 + 2x - 5x - 2x^2 + 2}{(x-2)(x-1)(x+2)(x-2)(x+1)(x+2)}\), we will first simplify the numerator. 1. **Simplify the Numerator:** \[ 3x^2 + 2x - 5x - 2x^2 + 2 \] Combine like terms: \[ (3x^2 - 2x^2) + (2x - 5x...

1 year ago

To simplify the expression \[ \frac{3x^2 + 2x - 5x - 2x^2 + 2}{(x-2)(x-1)(x+2)(x-2)(x+1)(x+2)}, \] let's break it down step by step! ### Step 1: Simplify the Numerator We start with the numerator: \[ 3x^2 + 2x - 5x - 2x^2 + 2 \] We can combine the like te...

1 year ago

5. Find the sum. (4𝑝−2𝑝2+8)+(5𝑝2+2𝑝)+(7−3𝑝)

1 year ago

To find the sum of the expression \((4p - 2p^2 + 8) + (5p^2 + 2p) + (7 - 3p)\), we will first group and combine like terms. 1. Start by writing out the expression: \[ (4p - 2p^2 + 8) + (5p^2 + 2p) + (7 - 3p) \] 2. Next, combine all the terms together: \[...

1 year ago

6. Which of the following responses shows that polynomials form a closed system under multiplication? (1 3)((𝑥 4−2) 2𝑥3+𝑥2 5𝑥∙2 5∙3

1 year ago

To demonstrate that polynomials form a closed system under multiplication, we need to show that when two polynomials are multiplied, the result is also a polynomial. 1. **Identifying Polynomials**: Let's take some example polynomials: - \( P(x) = x^4 - 2...

1 year ago

Using%C2%A0the Commutative Property,%C2%A0prove that these algebraic expressions are equivalent. In 1–2 sentences, explain your result. Expression 1:%C2%A0 y⋅3x Expression 2:%C2%A0 3xy

1 year ago

To prove that \( y \cdot 3x \) is equivalent to \( 3xy \) using the Commutative Property, we can rearrange the factors in the first expression: 1. \( y \cdot 3x = 3 \cdot y \cdot x \) (by factoring out the 3). 2. By the Commutative Property of multiplicat...

1 year ago

Your proof that \( y \cdot 3x \) is equivalent to \( 3xy \) using the Commutative Property is clear and correct. Here’s a brief recap and more details to reinforce the steps: 1. Starting with the expression: \[ y \cdot 3x \] we can rewrite it by factoring...

1 year ago

To demonstrate that Expression 1 is equivalent to Expression 2 using the Associative Property, we can rewrite both expressions and see if they simplify to the same result. ### Expression 1: \[ 22r - 13 \] ### Expression 2: \[ 19r + (3r - 2) - 11 \] First,...

1 year ago

e the Distributive Property to prove that these algebraic expressions are equivalent. Explain your answer in one sentence for each expression and show your work. Expression 1:%C2%A0 (x−5)(x+3) Expression 2:%C2%A0 2x2−x2−2x−20+5

1 year ago

To prove that the two algebraic expressions \((x - 5)(x + 3)\) and \(2x^2 - x^2 - 2x - 20 + 5\) are equivalent using the Distributive Property, we'll expand Expression 1 and simplify Expression 2. **Expression 1: \((x - 5)(x + 3)\)** Using the Distributiv...

1 year ago

To demonstrate how multiplying polynomials is a closed system, we'll multiply the two polynomials \( (x^2 - 1)(-2x + 5) \) and show that the result is also a polynomial. Let's perform the multiplication step-by-step: 1. **Distribute each term in the first...

1 year ago

To demonstrate that multiplying polynomials is a closed system, we'll multiply the polynomials \( (x^2 - 1)(-2x + 5) \): 1. **Distribute:** Using the distributive property, we have: \[ (x^2 - 1)(-2x + 5) = x^2 \cdot (-2x) + x^2 \cdot 5 - 1 \cdot (-2x) - 1...

1 year ago