Question

The expression (3x-4y^2)(3x+4y^2) is equivalent to:

Answer 1

The expression (3x-4y^2)(3x+4y^2) simplifies to 9x^2 - 16y^4 by applying the difference of squares rule, which is the square of the first term minus the square of the second term.

Step-by-step explanation:

The expression (3x-4y^2)(3x+4y^2) is an example of a difference of squares. This is a special product form in algebra where two binomials that are exactly the same except for a minus sign between the terms in one binomial and a plus sign in the other are multiplied together. The product of a difference of squares is always the square of the first term minus the square of the second term.

So, for the expression (3x-4y^2)(3x+4y^2), we apply this rule and get:

• First, square the first term of one of the binomials: (3x)^2 = 9x^2
• Then, square the second term of one of the binomials: (-4y^2)^2 = 16y^4
• Subtract the square of the second term from the square of the first term: 9x^2 - 16y^4

Therefore, the equivalent expression is 9x^2 - 16y^4.

Answer 2

`(3x-4y^2)(3x+4y^2)=(3x)^2-(4y^2)^2=9x^2-16y^4`