%5E2.jpeg "(3a-4b)^2")
Understanding (3a - 4b)^2
The expression (3a - 4b)^2 represents the square of the binomial (3a - 4b). To understand and simplify this expression, we need to recall the concept of squaring a binomial.
Squaring a Binomial
When we square a binomial, we multiply it by itself. For example, (x + y)^2 is the same as (x + y) * (x + y). To expand this, we use the FOIL method:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of each binomial.
- Inner: Multiply the inner terms of each binomial.
- Last: Multiply the last terms of each binomial.
Expanding (3a - 4b)^2
Applying the FOIL method to (3a - 4b)^2:
- First: (3a) * (3a) = 9a^2
- Outer: (3a) * (-4b) = -12ab
- Inner: (-4b) * (3a) = -12ab
- Last: (-4b) * (-4b) = 16b^2
Combining the terms, we get:
(3a - 4b)^2 = 9a^2 - 12ab - 12ab + 16b^2
Simplifying by combining the like terms:
(3a - 4b)^2 = 9a^2 - 24ab + 16b^2
Key Points
- The expression (3a - 4b)^2 represents the product of (3a - 4b) and itself.
- Expanding the expression requires applying the FOIL method.
- The simplified form of (3a - 4b)^2 is 9a^2 - 24ab + 16b^2.