Final answer:
To find the value of the variable, we need to expand and simplify the expression. Using the distributive property and combining like terms will help us find the value.
Step-by-step explanation:
To find the value of the variable in the expression (82 - 4g)(7g + 51), we need to expand and simplify the expression. First, use the distributive property to multiply 82 by both terms inside the second parentheses, and multiply -4g by both terms inside the first parentheses.
This gives us (-4g)(7g) + (-4g)(51) + (82)(7g) + (82)(51). Simplify each of these terms and combine like terms if possible to find the value of the variable.
Expanding the expression gives us -28g^2 - 204g + 574g + 4182. Combining like terms gives us -28g^2 + 370g + 4182. So the value of the variable is -28g^2 + 370g + 4182.