(2x+3)(4x^2-6x+9)-2(4x^3-1)

2 min read Jun 16, 2024

Simplifying the Expression: (2x+3)(4x^2-6x+9)-2(4x^3-1)

This expression involves expanding and combining terms. Let's break it down step by step:

1. Expanding the First Part

The first part of the expression, (2x+3)(4x^2-6x+9), is a product of two binomials. We can expand this using the FOIL method:

First terms: (2x)(4x^2) = 8x^3
Outer terms: (2x)(9) = 18x
Inner terms: (3)(-6x) = -18x
Last terms: (3)(9) = 27

Combining these terms, we get:

(2x+3)(4x^2-6x+9) = 8x^3 + 18x - 18x + 27

Notice that the middle terms cancel out.

2. Expanding the Second Part

The second part of the expression, -2(4x^3-1), involves simple distribution:

-2(4x^3-1) = -8x^3 + 2

3. Combining the Expanded Parts

Now, we can combine the expanded parts from steps 1 and 2:

(2x+3)(4x^2-6x+9)-2(4x^3-1) = (8x^3 + 18x - 18x + 27) + (-8x^3 + 2)

4. Simplifying the Expression

Finally, we combine like terms:

8x^3 - 8x^3 + 18x - 18x + 27 + 2 = 29

Conclusion

Therefore, the simplified form of the expression (2x+3)(4x^2-6x+9)-2(4x^3-1) is 29. This shows that the original expression simplifies to a constant value, meaning it is independent of the value of 'x'.