(x+7)^2+6(x^2-10)

Jasonbradley

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Jun 17, 2024

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Simplifying the Expression: (x+7)^2 + 6(x^2 - 10)

This article will guide you through simplifying the algebraic expression: (x+7)^2 + 6(x^2 - 10). We will break down the steps involved in expanding and combining like terms to reach a simplified form.

Expanding the Expression

1. Expanding the Square: We begin by expanding the squared term, (x+7)^2. Remember that squaring a binomial means multiplying it by itself:

   (x+7)^2 = (x+7)(x+7)

   To multiply these binomials, we can use the FOIL method (First, Outer, Inner, Last):

   • First: x * x = x^2
   • Outer: x * 7 = 7x
   • Inner: 7 * x = 7x
   • Last: 7 * 7 = 49

   Combining the terms, we get: x^2 + 7x + 7x + 49 = x^2 + 14x + 49

2. Expanding the Second Term: Next, we distribute the 6 to the terms inside the parentheses:

   6(x^2 - 10) = 6x^2 - 60

Combining Like Terms

Now, we can combine the terms we expanded in the previous steps:

(x+7)^2 + 6(x^2 - 10) = (x^2 + 14x + 49) + (6x^2 - 60)

Combine the x^2 terms, the x terms, and the constant terms:

= x^2 + 6x^2 + 14x + 49 - 60

= 7x^2 + 14x - 11

Conclusion

Therefore, the simplified form of the expression (x+7)^2 + 6(x^2 - 10) is 7x^2 + 14x - 11. This process involves expanding the squared term, distributing, and combining like terms to reach a simplified expression.