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Chapter 0: Problem 86

Perform the indicated operation or operations. $$(3 x+5)(2 x-9)-(7 x-2)(x-1)$$

Short Answer

Expert verified
The simplified expression is \(-x^2 -8x -47\).

Step by step solution

01

Apply FOIL method on the first pair

We first concentrate on \((3x+5)(2x-9)\). We apply FOIL which stands for First, Outer, Inner, Last i.e., we have \(3x * 2x\) (First), \(3x * -9\) (Outer), \(5 * 2x\) (Inner), \(5 * -9\) (Last). Solving these, we get \(6x^2 - 27x + 10x - 45\), which simplifies to \(6x^2 -17x -45\).
02

Apply FOIL method on the second pair

Next, we focus on \((7x-2)(x-1)\). Again, using FOIL, we have \(7x * x\) (First), \(7x * -1\) (Outer), \(-2 * x\) (Inner), \(-2 * -1\) (Last). Solving these, we get \(7x^2 -7x -2x + 2\), which simplifies to \(7x^2 -9x + 2\).
03

Subtraction

Now, subtract the expression from step 2 from the expression in step 1. So \((6x^2 -17x -45) - (7x^2 -9x +2)\). Be careful with the signs here. The expression simplifies to \(-x^2 -8x -47\).

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