(2 −10)(3 −9)(2x−10)(3x−9)

2 min read Jun 16, 2024

Factoring and Simplifying the Expression (2 −10)(3 −9)(2x−10)(3x−9)

This expression involves several multiplications of terms. We can simplify it by factoring out common factors and performing the multiplications.

Factoring the Constants

Let's start by factoring the constant terms:

(2 − 10): This can be simplified to -8.
(3 − 9): This simplifies to -6.

Now our expression looks like this:

(-8)(-6)(2x-10)(3x-9)

Factoring the Binomials

Next, we can factor out common factors from the binomials:

(2x - 10): We can factor out a 2: 2(x-5)
(3x - 9): We can factor out a 3: 3(x-3)

Our expression is now:

(-8)(-6)(2(x-5))(3(x-3))

Simplifying

Finally, we can multiply all the constants and rearrange the terms:

(-8)(-6)(2)(3)(x-5)(x-3) = 288(x-5)(x-3)

Conclusion

The simplified expression for (2 −10)(3 −9)(2x−10)(3x−9) is 288(x-5)(x-3). This form is useful for various applications, such as solving equations, finding roots, or performing further algebraic manipulations.