(3y-7)^2

2 min read Jun 16, 2024
(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:

  1. First: Multiply the first terms of each binomial: 3y * 3y = 9y^2
  2. Outer: Multiply the outer terms of the binomials: 3y * -7 = -21y
  3. Inner: Multiply the inner terms of the binomials: -7 * 3y = -21y
  4. 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.

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