Final answer:
The expression (3x – 4y)(3x + 4y) simplifies to 9x² - 16y², using the difference of squares formula. This is because the two binomials are conjugates, resulting in the square of the first term minus the square of the second term.
Step-by-step explanation:
To find the equivalent expression for (3x – 4y)(3x + 4y), we can use the distributive property of multiplication over addition. This means we need to multiply each term in the first expression (3x – 4y) by each term in the second expression (3x + 4y). Using FOIL method, we get:
(3x – 4y)(3x + 4y) = 3x * 3x + 3x * 4y - 4y * 3x - 4y * 4y
Simplifying this, we get:
(3x – 4y)(3x + 4y) = 9x^2 - 12xy - 12xy - 16y^2
Combining like terms, we get:
(3x – 4y)(3x + 4y) = 9x^2 - 24xy - 16y^2