Math Problem Statement

(5x^2 - 12x + 4) - (x^2 - 4x)

Solution

The expression in the image is:

(5x212x+4)(x24x)(5x^2 - 12x + 4) - (x^2 - 4x)

Let's simplify it step by step.

Step 1: Distribute the negative sign

Apply the negative sign to each term inside the second parentheses:

=(5x212x+4)x2+4x= (5x^2 - 12x + 4) - x^2 + 4x

Step 2: Combine like terms

Now, combine the terms with the same powers of xx.

  • Combine the x2x^2 terms: 5x2x2=4x25x^2 - x^2 = 4x^2
  • Combine the xx terms: 12x+4x=8x-12x + 4x = -8x
  • The constant term remains 44.

Thus, the simplified expression is:

4x28x+44x^2 - 8x + 4

This is the fully simplified version of the expression.

Would you like further details or explanations on any part of this process?

Here are 5 related questions to consider:

  1. How do you solve quadratic equations like 4x28x+4=04x^2 - 8x + 4 = 0?
  2. Can you factor the quadratic expression 4x28x+44x^2 - 8x + 4?
  3. What is the vertex form of a quadratic expression, and how can you find it?
  4. How do you find the roots of the quadratic equation 4x28x+4=04x^2 - 8x + 4 = 0 using the quadratic formula?
  5. How can you complete the square for the quadratic 4x28x+44x^2 - 8x + 4?

Tip: Always check for common factors in simplified expressions—sometimes the entire expression can be factored further!