To expand the expression \((7x + 3)^2\), we use the formula for the square of a binomial:

\[
(a + b)^2 = a^2 + 2ab + b^2
\]

Here, \(a = 7x\) and \(b = 3\). Applying the formula, we get:

\[
(7x + 3)^2 = (7x)^2 + 2 \cdot (7x) \cdot 3 + 3^2
\]

Now, calculate each term:

1. \((7x)^2 = 49x^2\)
2. \(2 \cdot (7x) \cdot 3 = 42x\)
3. \(3^2 = 9\)

Putting it all together, we have:

\[
(7x + 3)^2 = 49x^2 + 42x + 9
\]

Would you like more details or have any questions? Here are some more questions you might be interested in:

1. How do you expand \((x + 5)^2\)?
2. What is the derivative of \(49x^2 + 42x + 9\)?
3. How do you solve the quadratic equation \(49x^2 + 42x + 9 = 0\)?
4. What are the roots of \(49x^2 + 42x + 9 = 0\)?
5. How do you factor the expression \(49x^2 + 42x + 9\)?

**Tip:** Always double-check your work by substituting back into the original equation to ensure it holds true.

Learn how to expand the expression (7x + 3)^2 using the square of a binomial formula. This detailed step-by-step solution covers the key algebraic concept of binomial expansion and is suitable for Grades 7-9 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation