Video: Using the Distributive Property of Multiplication to Expand Expressions Containing Brackets

Expand and simplify (2π‘₯ βˆ’ 2)(6 βˆ’ π‘₯) + (π‘₯ βˆ’ 4)(π‘₯ βˆ’ 5).

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Video Transcript

Expand and simplify two π‘₯ minus two times six minus π‘₯ plus π‘₯ minus four times π‘₯ minus five.

First, we need to use the distributive property, and we need to foil. Two π‘₯ times six is 12π‘₯. Two π‘₯ times negative π‘₯ is negative two π‘₯ squared. Negative two times six is negative 12. And negative two times negative π‘₯ is positive two π‘₯. Bring down our addition sign. π‘₯ times π‘₯ is π‘₯ squared. π‘₯ times negative five is negative five π‘₯. Negative four times π‘₯ is negative four π‘₯, 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 π‘₯ squared plus π‘₯ squared. That would be negative one π‘₯ squared or negative π‘₯ squared. Now let’s add the Twelve π‘₯ plus two π‘₯ minus five π‘₯ minus four π‘₯ is equal to five π‘₯.

And now our constants, negative 12 plus 20 is eight. So our final answer: negative π‘₯ squared plus five π‘₯ plus eight.

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