(x+5)(x+6)(x+7) Simplify

Jasonbradley

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Jun 16, 2024

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Simplifying (x+5)(x+6)(x+7)

This expression represents the product of three binomials. To simplify it, we can use the distributive property multiple times.

Step 1: Multiply the first two binomials

First, let's multiply (x+5) and (x+6):

(x+5)(x+6) = x(x+6) + 5(x+6) = x² + 6x + 5x + 30 = x² + 11x + 30

Step 2: Multiply the result by the third binomial

Now we have: (x² + 11x + 30)(x+7)

Let's multiply again: x²(x+7) + 11x(x+7) + 30(x+7) = x³ + 7x² + 11x² + 77x + 30x + 210

Step 3: Combine like terms

Finally, combining the like terms:

x³ + 18x² + 107x + 210

Conclusion

Therefore, the simplified form of (x+5)(x+6)(x+7) is x³ + 18x² + 107x + 210.