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(x+4y)^2

2 min read Jun 16, 2024
(x+4y)^2

Expanding (x + 4y)^2

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

Using FOIL

FOIL stands for First, Outer, Inner, Last. This method involves multiplying each term in the first binomial by each term in the second binomial.

Here's how it works for (x + 4y)^2:

  1. First: x * x = x^2
  2. Outer: x * 4y = 4xy
  3. Inner: 4y * x = 4xy
  4. Last: 4y * 4y = 16y^2

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

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

Using the Square of a Binomial Formula

The square of a binomial formula states: (a + b)^2 = a^2 + 2ab + b^2

Applying this to our expression, we have:

(x + 4y)^2 = x^2 + 2(x)(4y) + (4y)^2

Simplifying: x^2 + 8xy + 16y^2

Conclusion

Both methods lead to the same expanded form of (x + 4y)^2: x^2 + 8xy + 16y^2. Choose the method that you find easier to understand and apply.

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