\left(3x+4\right)^2-\left(3x-2\right)\left(3x-8\right)

Let's simplify the given expression:

\[
\left(3x+4\right)^2 - \left(3x-2\right)\left(3x-8\right)
\]

### Step 1: Expand \(\left(3x+4\right)^2\)
\[
\left(3x+4\right)^2 = (3x+4)(3x+4) = 9x^2 + 12x + 12x + 16 = 9x^2 + 24x + 16
\]

### Step 2: Expand \(\left(3x-2\right)\left(3x-8\right)\)
\[
\left(3x-2\right)\left(3x-8\right) = (3x)(3x) + (3x)(-8) + (-2)(3x) + (-2)(-8)
\]
\[
= 9x^2 - 24x - 6x + 16 = 9x^2 - 30x + 16
\]

### Step 3: Substitute the expanded forms back into the original expression
\[
(9x^2 + 24x + 16) - (9x^2 - 30x + 16)
\]

### Step 4: Simplify the expression
\[
9x^2 + 24x + 16 - 9x^2 + 30x - 16
\]
\[
= (9x^2 - 9x^2) + (24x + 30x) + (16 - 16)
\]
\[
= 0 + 54x + 0 = 54x
\]

### Final answer:
\[
54x
\]

Would you like more details on any step or have any questions?

Here are 5 related questions:
1. How do you expand the square of a binomial?
2. What is the distributive property of multiplication over addition?
3. How do you combine like terms in an algebraic expression?
4. How do you solve quadratic expressions involving two binomials?
5. Can the result of this expression be factored further?

**Tip:** Always double-check your sign operations when expanding and simplifying algebraic expressions!

Explore the step-by-step solution to simplify the algebraic expression (3x+4)^2 - (3x-2)(3x-8). This solution covers key algebraic concepts, including binomial expansion and combining like terms. Ideal for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation