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(y-4)^2 Expand

2 min read Jun 17, 2024
(y-4)^2 Expand

Expanding (y-4)^2

The expression (y-4)^2 represents the square of the binomial (y-4). To expand it, we can use the FOIL method or the square of a binomial pattern.

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last. This method helps us multiply two binomials together:

  1. First: Multiply the first terms of each binomial: y * y = y^2
  2. Outer: Multiply the outer terms: y * -4 = -4y
  3. Inner: Multiply the inner terms: -4 * y = -4y
  4. Last: Multiply the last terms: -4 * -4 = 16

Now, combine the terms: y^2 - 4y - 4y + 16

Finally, simplify by combining like terms: y^2 - 8y + 16

Using the Square of a Binomial Pattern

The square of a binomial pattern states that: (a - b)^2 = a^2 - 2ab + b^2

In our case, a = y and b = 4. Applying the pattern, we get:

y^2 - 2(y)(4) + 4^2

Simplifying, we obtain: y^2 - 8y + 16

Conclusion

Both methods lead to the same result: (y-4)^2 = y^2 - 8y + 16. Expanding a squared binomial is a fundamental skill in algebra, particularly useful for solving equations and simplifying expressions.

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