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Chapter 5: Problem 94

Perform the indicated operations. $$(x+5)(x-6)-(x+2)(x-9)$$

Short Answer

Expert verified
The result of the operation \((x+5)(x-6)-(x+2)(x-9)\) is \(6x - 12\).

Step by step solution

01

Expand the Binomials

Expand each binomial using the distributive property or the FOIL method. So, \((x+5)(x-6)\) becomes \(x^2 - 6x + 5x - 30\) and \((x+2)(x-9)\) becomes \(x^2 - 9x + 2x - 18\). After simplifying, the two expressions become \(x^2 - x - 30\) and \(x^2 - 7x - 18\) respectively.
02

Perform the Subtraction

Subtract the second expanded expression from the first. The operation then becomes \((x^2 - x - 30) - (x^2 -7x -18)\). Remove the parentheses, remembering to multiply each term by -1 from the second parentheses because of the subtraction operation. This gives \(x^2 - x - 30 - x^2 +7x + 18\).
03

Combine Like Terms

Combine the like terms: \(x^2 - x^2 + (-x + 7x) + (-30 + 18)\), which simplifies to \(6x - 12\).

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