%5E2.jpeg "(3y-7)^2")
Expanding (3y - 7)^2
The expression (3y - 7)^2 represents the square of the binomial (3y - 7). To expand this, we can use the following methods:
Method 1: Using the FOIL method
FOIL stands for First, Outer, Inner, Last. This method helps us multiply two binomials:
- First: Multiply the first terms of each binomial: 3y * 3y = 9y^2
- Outer: Multiply the outer terms of the binomials: 3y * -7 = -21y
- Inner: Multiply the inner terms of the binomials: -7 * 3y = -21y
- Last: Multiply the last terms of each binomial: -7 * -7 = 49
Now, combine the results: 9y^2 - 21y - 21y + 49
Finally, simplify by combining like terms: 9y^2 - 42y + 49
Method 2: Using the square of a binomial formula
The square of a binomial formula states: (a - b)^2 = a^2 - 2ab + b^2
In this case, a = 3y and b = 7.
Substituting the values into the formula, we get:
(3y - 7)^2 = (3y)^2 - 2(3y)(7) + (7)^2
Expanding the terms, we get:
9y^2 - 42y + 49
Both methods result in the same expanded form: 9y^2 - 42y + 49.
This expanded form is a quadratic expression and can be used for further algebraic manipulations or solving equations.