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anonymous
 one year ago
Part A: The area of a square is (9x2 − 12x + 4) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points)
Part B: The area of a rectangle is (25x2 − 16y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)
anonymous
 one year ago
Part A: The area of a square is (9x2 − 12x + 4) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points) Part B: The area of a rectangle is (25x2 − 16y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)

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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Part A. Factor 9x2 − 12x + 4 This trinomial follows the pattern \(a^2  2ab + b^2 = (a  b)^2\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok im gonna plug it in

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2To factor it, first, what is it whose square is to 9x^2?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2What do you square to get 9x^2? ___ * ___ = 9x^2 What is the square root of 9?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2What number times itself equals 9?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Good. What times itself is x^2?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2No. 1 * 1 = 1 The answer is x. x * x = x^2 Ok?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2That means (3x)(3x) = 9x^2 The square root of 9x^2 is 3x

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Now we deal with the 4. What is the square root of 4?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Good. Since we have the pattern: \(a^2  2ab + b^2 = (a  b)^2\) in this case we have: \(9x^2  12x + 4 = (3x  2)^2\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2That means the side of the square is 3x  2 units

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so thats the length of each side?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Yes. Since it's a square, all sides measure 3x  2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you help with B?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2In part B, you have a rectangle. A rectangle may or may not be a square. We need to factor (25x2 − 16y2)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Here, the pattern of the binomial is: \(a^2  b^2 = (a + b)(a  b) \) This is called the difference of two squares.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2You are correct. As you can see the sides are not equal, so this rectangle is not a square.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Two opposite sides have length 5x + 4y, and the other two opposite sides have length 5x  4y
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