(3x+4y-5p)2

Jasonbradley

3 min read

·

Jun 16, 2024

11

Share

Expanding the Square of (3x + 4y - 5p)

The expression **(3x + 4y - 5p)**² represents the square of a trinomial. To expand this expression, we'll utilize the distributive property and the concept of binomial squares.

Understanding the Basics

Before diving into the expansion, let's review some key principles:

• Distributive Property: This property states that multiplying a sum by a number is the same as multiplying each term of the sum by the number individually. For example: a(b + c) = ab + ac.
• Binomial Squares: The square of a binomial can be expanded using the formula: (a + b)² = a² + 2ab + b².

Expanding the Expression

1. Rewrite the Expression: We can rewrite (3x + 4y - 5p)² as [(3x + 4y) - 5p]². This helps visualize the expression as a binomial squared, with (3x + 4y) representing one term and 5p representing the other.

2. Apply the Binomial Square Formula: Now we can apply the formula: [(3x + 4y) - 5p]² = (3x + 4y)² - 2(3x + 4y)(5p) + (5p)².

3. Expand Further: We need to expand the remaining squares and products:

   • (3x + 4y)²: Using the binomial square formula again, we get (3x)² + 2(3x)(4y) + (4y)² = 9x² + 24xy + 16y²
   • - 2(3x + 4y)(5p): Distribute the -10p to both terms inside the parentheses: -10p(3x) - 10p(4y) = -30xp - 40yp
   • (5p)²: Simplifying, we get 25p².

4. Combine Terms: Putting all the expanded terms together, we have:

   (3x + 4y - 5p)² = 9x² + 24xy + 16y² - 30xp - 40yp + 25p²

Conclusion

By applying the distributive property and the formula for binomial squares, we have successfully expanded the expression (3x + 4y - 5p)². The final result is a polynomial with six terms: 9x² + 24xy + 16y² - 30xp - 40yp + 25p².