*standard form of* 3(5*x*+3)(5*x*−3)​

To express \( 3(5x + 3)(5x - 3) \) in standard form, we first apply the difference of squares formula:

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

In this case, \( a = 5x \) and \( b = 3 \). Therefore,

\[
(5x + 3)(5x - 3) = (5x)^2 - 3^2 = 25x^2 - 9
\]

Now, multiply the result by 3:

\[
3(25x^2 - 9) = 75x^2 - 27
\]

Thus, the expression in standard form is:

\[
75x^2 - 27
\]

Would you like a detailed explanation of any step or have any further questions?

### Related Questions:
1. How do you expand products of binomials using the distributive property?
2. What is the difference of squares, and how is it applied?
3. How can you simplify expressions involving polynomials?
4. What is the standard form of a quadratic equation?
5. How do you factor expressions like \( 75x^2 - 27 \)?

### Tip:
The difference of squares is a powerful technique used frequently in factoring quadratic expressions. It’s good to recognize its structure when simplifying expressions.

Learn how to convert the expression 3(5x + 3)(5x - 3) into its standard form using the difference of squares formula. This problem involves key algebraic concepts, including quadratic expressions and the application of the difference of squares. Suitable for students in Grades 8-10.

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