(x+2)(x+8)+(4x^2+8x-3)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (x+2)(x+8)+(4x^2+8x-3)

This article will walk through the steps to simplify the given expression: (x+2)(x+8)+(4x^2+8x-3). We will use the distributive property and combining like terms to arrive at a simplified polynomial.

Step 1: Expand the product of the binomials

First, we need to expand the product of the two binomials: (x+2)(x+8). We can do this using the FOIL method (First, Outer, Inner, Last):

• First: x * x = x^2
• Outer: x * 8 = 8x
• Inner: 2 * x = 2x
• Last: 2 * 8 = 16

Combining these terms, we get: x^2 + 8x + 2x + 16 = x^2 + 10x + 16

Now our expression becomes: x^2 + 10x + 16 + (4x^2 + 8x - 3)

Step 2: Combine like terms

We can now combine the terms with the same power of x:

• x^2 terms: x^2 + 4x^2 = 5x^2
• x terms: 10x + 8x = 18x
• Constant terms: 16 - 3 = 13

Final Simplified Expression

Combining all these terms, we arrive at our simplified expression:

5x^2 + 18x + 13