Math Problem Statement

Which expression is the product of (4x + 3) and (x2 + 7x − 2)

Solution

To find the product of the expressions (4x+3)(4x + 3) and (x2+7x2)(x^2 + 7x - 2), we need to distribute each term in the first expression to each term in the second expression.

Here’s the step-by-step process:

  1. Distribute 4x4x to each term in x2+7x2x^2 + 7x - 2: 4xx2+4x7x+4x(2)4x \cdot x^2 + 4x \cdot 7x + 4x \cdot (-2) =4x3+28x28x= 4x^3 + 28x^2 - 8x

  2. Distribute 33 to each term in x2+7x2x^2 + 7x - 2: 3x2+37x+3(2)3 \cdot x^2 + 3 \cdot 7x + 3 \cdot (-2) =3x2+21x6= 3x^2 + 21x - 6

  3. Combine all the terms together: 4x3+28x28x+3x2+21x64x^3 + 28x^2 - 8x + 3x^2 + 21x - 6

  4. Combine like terms: 4x3+(28x2+3x2)+(8x+21x)64x^3 + (28x^2 + 3x^2) + (-8x + 21x) - 6 =4x3+31x2+13x6= 4x^3 + 31x^2 + 13x - 6

So, the product of (4x+3)(4x + 3) and (x2+7x2)(x^2 + 7x - 2) is:

4x3+31x2+13x64x^3 + 31x^2 + 13x - 6

Would you like more details or have any questions? Here are some questions you might want to ask:

  1. How do you factor polynomial expressions?
  2. Can you explain the distributive property in algebra?
  3. What are like terms and how do you combine them?
  4. How do you solve quadratic equations?
  5. What is the difference between polynomial and rational expressions?

Tip: When multiplying polynomials, always ensure to distribute each term in the first polynomial to every term in the second polynomial to avoid missing any terms.

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Math Problem Analysis

Mathematical Concepts

Polynomials
Algebra

Formulas

Distributive property

Theorems

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Suitable Grade Level

Grades 7-9