Final answer:
The final answer to the equation (y+z)² - 3x + 8 is y² + 2yz + z² - 3x + 8.
Step-by-step explanation:
The given equation, (y+z)² - 3x + 8, can be expanded using the formula for the square of a binomial, which is (a + b)² = a² + 2ab + b². Applying this formula to the given expression, we get:
(y+z)² = y² + 2yz + z².
Now, substitute this back into the original equation:
y² + 2yz + z² - 3x + 8.
This is the expanded form of the given equation. Each term in the expansion represents a specific mathematical operation. The first term, y², comes from squaring the y term in the binomial. The second term, 2yz, comes from multiplying the y and z terms by 2. The third term, z², comes from squaring the z term. The fourth term, -3x, is unchanged from the original equation, and the last term, 8, remains constant.
In summary, the final answer to the equation is y² + 2yz + z² - 3x + 8, which is obtained by applying the square of a binomial formula to the given expression. This expanded form provides a clear representation of each term's contribution to the overall result.