%5E2.jpeg "(7y)^2")
Understanding (7y)^2
In mathematics, (7y)^2 represents the square of the entire expression 7y. This means we are multiplying the expression by itself:
(7y)^2 = (7y) * (7y)
To simplify this, we can use the distributive property of multiplication:
(7y) * (7y) = 7 * y * 7 * y
Rearranging the terms, we get:
7 * 7 * y * y = 49 * y^2
Therefore, (7y)^2 is equivalent to 49y^2.
Key Points to Remember:
- Squaring an expression means multiplying it by itself.
- The distributive property allows us to expand the expression.
- The exponent applies to both the coefficient (7) and the variable (y).
Example Application:
Let's say we have the expression (7y)^2 and we want to find its value when y = 2.
- Substitute y = 2: (7 * 2)^2
- Simplify the multiplication: (14)^2
- Calculate the square: 14 * 14 = 196
Therefore, when y = 2, the value of (7y)^2 is 196.
Conclusion:
Understanding the concept of squaring expressions like (7y)^2 is crucial in simplifying algebraic expressions and solving equations. By applying the distributive property and understanding how exponents work, we can easily evaluate and simplify such expressions.