Final answer:
The simplified expression of (4372 + 297 - 2y) - (-771 + 6z - 2y) is 3898 - 4y + 6z, with the numerical coefficient being 3898, -4 as the coefficient for y, and 6 as the coefficient for z.
Step-by-step explanation:
To find the expression for (4372 + 297 - 2y) - (-771 + 6z - 2y), we first simplify each term separately and then subtract the second expression from the first. Simplifying the terms inside the parentheses gives us:
- The first term simplifies to 4372 + 297 - 2y, which is 4669 - 2y when combining the numerical terms.
- The second term simplifies to -(-771 + 6z - 2y), which becomes 771 - 6z + 2y when distributive property of multiplication over subtraction is applied, negating each term inside the parentheses.
Subtracting the second expression from the first, we get:
(4669 - 2y) - (771 - 6z + 2y)
Expand the subtraction by changing the sign of each term in the second expression and combining like terms:
- 4669 - 2y - 771 + 6z - 2y = 4669 - 771 - 2y - 2y + 6z
- Combining numerical terms and the terms with y, we get 3898 - 4y + 6z.
Therefore, the simplified expression is 3898 - 4y + 6z, with coefficients 3898 for the constant, -4 for y, and 6 for z.