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Bethani Gasparine

Expand and simplify (2𝑥 − 2)(6 − 𝑥) + (𝑥 − 4)(𝑥 − 5).

Expand and simplify two 𝑥 minus two times six minus 𝑥 plus 𝑥 minus four times 𝑥 minus five.

First, we need to use the distributive property, and we need to foil. Two 𝑥 times six is 12𝑥. Two 𝑥 times negative 𝑥 is negative two 𝑥 squared. Negative two times six is negative 12. And negative two times negative 𝑥 is positive two 𝑥. Bring down our addition sign. 𝑥 times 𝑥 is 𝑥 squared. 𝑥 times negative five is negative five 𝑥. Negative four times 𝑥 is negative four 𝑥, and negative four times negative five is positive 20. So now we need to combine like terms. Let’s start with the highest exponents; that’s the squareds.

So we have negative two 𝑥 squared plus 𝑥 squared. That would be negative one 𝑥 squared or negative 𝑥 squared. Now let’s add the Twelve 𝑥 plus two 𝑥 minus five 𝑥 minus four 𝑥 is equal to five 𝑥.

And now our constants, negative 12 plus 20 is eight. So our final answer: negative 𝑥 squared plus five 𝑥 plus eight.

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