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The area of a rectangle is (16x2 − 9y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely.
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Okay so you know that in order to solve the problem you would need to factor\[16x^2 - 9y^2\]
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What I do when I see these type of equations is to see if the numbers in front of the x and y can be square rooted.
16 and 9 can be square rooted to 4 and 3 so let's split the equation starting with that.
\[(4x \pm 3y) (4x \pm 3y)\]
I put a plus and minus sign in the middle so we can determine what sign we should use.
What is that symbol?
Just pretend that symbol is a box. We need to figure out what sign to put in the middle. That's why I put that. Don't let that sign confuse you okay?
Since the actual equation has a minus sign in the middle that means the two equations have to cancel out the middle term of that equation. The middle term, for example, can be seen in the equation below:\[ax^2 +bx +c\] The term "bx is the middle term. The question however doesn't give us a middle term because it is saying that the middle term is 0.
I'll give you 3 answer choices. Tell me which equation will cancel out the middle term for the question that was given to you\[16x^2-9y^2\]A.) (4x + 3y) (4x +3y)
B.) (4x + 3y) (4x - 3y)
C.) (4x - 3y) (4x - 3y)
One of these answers can cancel out the middle term. Do you know how to factor equations? That can help when finding which choice it will be.