(y+8)^2

Jasonbradley

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Jun 17, 2024

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Expanding (y + 8)^2

The expression (y + 8)^2 represents the square of the binomial (y + 8). To expand this expression, we can use the FOIL method or the square of a binomial formula.

Using FOIL Method

FOIL stands for First, Outer, Inner, Last. It helps us multiply two binomials systematically.

1. First: Multiply the first terms of each binomial: y * y = y^2
2. Outer: Multiply the outer terms of the binomials: y * 8 = 8y
3. Inner: Multiply the inner terms of the binomials: 8 * y = 8y
4. Last: Multiply the last terms of each binomial: 8 * 8 = 64

Now, add all the products together: y^2 + 8y + 8y + 64

Finally, combine the like terms: y^2 + 16y + 64

Using Square of a Binomial Formula

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

In this case, a = y and b = 8. Substitute these values into the formula:

y^2 + 2(y)(8) + 8^2

Simplify the expression: y^2 + 16y + 64

Conclusion

Both methods result in the same expanded form of (y + 8)^2, which is y^2 + 16y + 64. This expansion is useful in various algebraic manipulations and problem-solving situations.