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(-5+v)2

2 min read Jun 16, 2024
(-5+v)2

Expanding (-5+v)<sup>2</sup>

This expression represents the square of a binomial, specifically the sum of -5 and the variable v. To expand it, we can apply the FOIL method or use the square of a binomial formula.

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last, and it helps us multiply two binomials:

  1. First: Multiply the first terms of each binomial: (-5) * (-5) = 25
  2. Outer: Multiply the outer terms of the binomials: (-5) * v = -5v
  3. Inner: Multiply the inner terms of the binomials: v * (-5) = -5v
  4. Last: Multiply the last terms of each binomial: v * v = v<sup>2</sup>

Now, add all the terms together: 25 - 5v - 5v + v<sup>2</sup>

Finally, combine the like terms: v<sup>2</sup> - 10v + 25

Using the Square of a Binomial Formula

The square of a binomial formula is: (a + b)<sup>2</sup> = a<sup>2</sup> + 2ab + b<sup>2</sup>

In our case, a = -5 and b = v. Applying the formula:

(-5 + v)<sup>2</sup> = (-5)<sup>2</sup> + 2(-5)(v) + v<sup>2</sup>

Simplifying: v<sup>2</sup> - 10v + 25

Conclusion

Both methods lead to the same expanded expression: v<sup>2</sup> - 10v + 25.

This demonstrates the versatility of applying different mathematical tools to solve the same problem.

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