(d+3)^2=

Jasonbradley

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Jun 16, 2024

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Expanding (d+3)^2

The expression (d+3)^2 represents the square of the binomial (d+3). To expand this expression, we can use the FOIL method or the square of a binomial formula.

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last. It helps us multiply two binomials by systematically multiplying each term in the first binomial with each term in the second binomial.

1. First: Multiply the first terms of each binomial: d * d = d^2
2. Outer: Multiply the outer terms of the binomials: d * 3 = 3d
3. Inner: Multiply the inner terms of the binomials: 3 * d = 3d
4. Last: Multiply the last terms of each binomial: 3 * 3 = 9

Now, combine the terms: d^2 + 3d + 3d + 9

Finally, simplify by combining like terms: d^2 + 6d + 9

Using the Square of a Binomial Formula

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

Applying this formula to (d+3)^2, we have:

a = d b = 3

Therefore: (d + 3)^2 = d^2 + 2(d)(3) + 3^2

Simplifying: d^2 + 6d + 9

Conclusion

Both methods lead to the same result: (d+3)^2 = d^2 + 6d + 9. This expanded form is useful for various algebraic manipulations and solving equations.