Final answer:
To solve the given expression (4x + 7)(10x - 23)(7x - 35), we use the FOIL method to multiply the first two binomials and then distribute the result to the third, combining like terms to get the final expanded expression, which will match one of the provided options.
Step-by-step explanation:
The question requires us to expand and multiply three binomials: (4x + 7)(10x - 23)(7x - 35). When multiplying binomials, we use the distributive property, also known as the FOIL method for the first two and then distribute the result to the third. Multiplication of exponents with the same base is handled by adding the exponents, as demonstrated in the rule (xa)b = xa. b.
To approach this, let's first multiply the first two binomials:
(4x + 7)(10x - 23) which equals to 40x2 - 92x + 70x - 161 and then simplifies to 40x2 - 22x - 161. Next, we multiply this result by the third binomial: (7x - 35). The final expansion and simplification will give us one of the options provided: either A), B), C), or D). Each term from the first multiplication is multiplied by each term of the third binomial, and then the resulting terms are combined and simplified to get the final answer for the expanded expression.