(-2x+5y-3z)2

Jasonbradley

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Jun 16, 2024

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Expanding (-2x + 5y - 3z)^2

This expression represents the square of a trinomial. To expand it, we can use the following steps:

Understanding the Concept:

The expression (-2x + 5y - 3z)^2 means multiplying the trinomial (-2x + 5y - 3z) by itself.

Expansion using FOIL (for the first two terms):

1. Multiply the first terms: (-2x) * (-2x) = 4x^2
2. Multiply the outer terms: (-2x) * (5y) = -10xy
3. Multiply the inner terms: (5y) * (-2x) = -10xy
4. Multiply the last terms: (5y) * (5y) = 25y^2

Expanding with the remaining term:

Now, we need to multiply the result we obtained above by (-3z) and add it to the previous terms.

1. Multiply the first term by (-3z): 4x^2 * (-3z) = -12x^2z
2. Multiply the second term by (-3z): -10xy * (-3z) = 30xyz
3. Multiply the third term by (-3z): -10xy * (-3z) = 30xyz
4. Multiply the fourth term by (-3z): 25y^2 * (-3z) = -75y^2z
5. Multiply the fifth term by (-3z): -12x^2z * (-3z) = 36x^2z^2
6. Multiply the sixth term by (-3z): 30xyz * (-3z) = -90xyz^2
7. Multiply the seventh term by (-3z): 30xyz * (-3z) = -90xyz^2
8. Multiply the eighth term by (-3z): -75y^2z * (-3z) = 225y^2z^2

Combining Like Terms:

Finally, we combine all the like terms to get the expanded form:

4x^2 + 25y^2 + 9z^2 - 20xy - 30xz - 50yz

Therefore, the expanded form of (-2x + 5y - 3z)^2 is 4x^2 + 25y^2 + 9z^2 - 20xy - 30xz - 50yz.