Many 1/2 inch cubes can fit into a box that is 15 inches tall, 1 1/2 inches wide, and 3 inches long?
1 answer:
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Answer:
Part A: The length of each side is units long.
Part B: The dimensions are 5x-4 and 5x+4 units long.
Step-by-step explanation:
Part A:
-->
--> Multiply 9 times 4 to see the factors of that product
--> 9 times4 = 36
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
Use the factor 6 and make it negative so -6
add another -6
Keep in mind that it is -6x
--> 9x^2-6x-6x+4
Separate the four terms into two different binomials
--> 9x^2-6x and -6x+4
Factor the binomials
With 9x^2-6x you can factor a 3x
So it will 3x(3x-2)
Do the same thing with -6x+4
You can factor out a -2
-2(3x-2)
The reason you factor out a -2 and not 2 is because it has to be same so in this case it is (3x-2)
Take the two numbers that you factored and put them to make an expression so (3x-2)
--> (3x-2)(3x-2) or (3x-2)^2
3x-2 is the length of each side so it is 3x-2 units long
Part B:
-->25x^2-16y^2
Use the difference of squares
take the square root of 25x^2
that is 5x
take the square root of 16y^2
that is 4y
write it in this way (5x+4y)(5x-4y)
These are the dimensions of the rectangle