Final answer:
The value of 'a' and 'b' in the given expression are determined by using the distributive property. After comparison and simplifying the coefficients and constant terms, we find that 'a' equals 5 and 'b' equals 35. This demonstrates algebraic manipulation rather than solving a quadratic equation.
Step-by-step explanation:
To find the values of a and b in the expression a(8x + 7) = 40x + b, we need to apply the distributive property, which states that for any three numbers, m, n, and p, the expression m(n + p) is equivalent to mn + mp. In this case, to apply the distributive property, we multiply 'a' with both 8x and 7, which gives us 8ax + 7a. To find 'a', we set 8ax equal to 40x because the coefficients of x must be equal on both sides of the equation if the two expressions are to be equivalent. This gives us 8a = 40, which simplifies to a = 5. To find 'b', we look at the constant terms. Since there is no constant term on the left side of the equation, 7a must equal b. Substituting the value of 'a' we found, we get b = 7a, which simplifies to b = 35. Therefore, the value of 'a' is 5, and the value of 'b' is 35.
The provided information about quadratic equations and the quadratic formula does not directly pertain to the question, as the expression in the question is not a quadratic equation but a simple algebraic expression in one variable, x.