Math Problem Statement

(2x + 3)(x + 3x)?

Solution

The expression in the image is:

(2x+3)(x+3x)(2x + 3)(x + 3x)

Let's simplify and solve this expression:

  1. First, simplify the expression inside the second parentheses: x+3xx + 3x. x+3x=4xx + 3x = 4x So, the expression now becomes: (2x+3)(4x)(2x + 3)(4x)

  2. Now, distribute 4x4x across the terms in 2x+32x + 3: (2x+3)(4x)=2x4x+34x(2x + 3)(4x) = 2x \cdot 4x + 3 \cdot 4x

  3. Calculate each term: 2x4x=8x22x \cdot 4x = 8x^2 34x=12x3 \cdot 4x = 12x

  4. Combine the results: 8x2+12x8x^2 + 12x

So, the simplified expression is:

8x2+12x8x^2 + 12x

Would you like more details or have any questions?

Here are some related questions you might consider:

  1. How would you solve 8x2+12x=08x^2 + 12x = 0?
  2. What happens if you factor out the common terms in the expression 8x2+12x8x^2 + 12x?
  3. How would this change if the original expression had a different constant term in either factor?
  4. What would the graph of y=8x2+12xy = 8x^2 + 12x look like?
  5. How can you use the quadratic formula to solve 8x2+12x=c8x^2 + 12x = c for some constant cc?

Tip: Always check for like terms when simplifying expressions, as they can often be combined to simplify your calculations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomials

Formulas

Distributive Property: (a + b)(c + d) = ac + ad + bc + bd

Theorems

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Suitable Grade Level

Grades 7-9