Question

Simplify the expression: 6x^3.y^4.z^y+10x^5.y^8.z^7

a. 16x^5.y^12.z^8
b. 16x^5.y^8.z^7
c. 6x^8.y^12.z^y
d. 10x^5.y^12.z^8

Answer 1

Main Answer:

The simplified expression for
`\(6x^3y^4z^y + 10x^5y^8z^7\) is \(16x^5y^8z^7\)`. (Option B).

Step-by-step explanation:

1. Start by combining like terms, which involves adding the coefficients of terms with the same variables and exponents.

2. For the
`\(x\)` terms:
`\(6x^3 + 10x^5 = 16x^5\)` since they share a common factor of
`\(x^3\)`.

3. For the
`\(y\)` terms:
`\(y^4 + y^8 = y^8\)` since they share a common factor of
`\(y^4\)`.

4. For the
`\(z\)` terms:
`\(z^y + z^7\)` cannot be combined since the exponents are different, so it remains
`\(z^y + z^7\)`.

5. Putting it all together, the simplified expression is
`\(16x^5y^8z^7\)`.

Therefore, the correct answer is (b)
`\(16x^5y^8z^7\)`.