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)

Part A: The area of a square is given by the expression $9x^2 - 12x + 4$ square units. To determine the length of each side, we need to factor this expression completely.

1. Recognize that the expression is a quadratic trinomial. We will factor it by finding two binomials that multiply to give the original expression.
2. The expression $9x^2 - 12x + 4$ can be rewritten as a perfect square trinomial. Notice that it fits the form $(ax - b)^2 = a^2x^2 - 2abx + b^2$.

Let's rewrite the expression: $9x^2 - 12x + 4 = (3x - 2)^2$

Therefore, the length of each side of the square is: $3x - 2$

Part B: The area of a rectangle is given by the expression $25x^2 - 16y^2$ square units. To determine the dimensions of the rectangle, we need to factor this expression completely.

1. Recognize that the expression is a difference of squares. The difference of squares can be factored using the formula $a^2 - b^2 = (a + b)(a - b)$.

Let's apply this formula: $25x^2 - 16y^2 = (5x)^2 - (4y)^2$ $= (5x + 4y)(5x - 4y)$

Therefore, the dimensions of the rectangle are: $5x + 4y$ and $5x - 4y$

Part A: The area of a square is given by the expression $9x^2 - 12x + 4$ square units. To determine the length of each side, we need to factor this expression completely.

1. Recognize that the expression is a quadratic trinomial. We will factor it by finding two binomials that multiply to give the original expression.
2. The expression $9x^2 - 12x + 4$ can be rewritten as a perfect square trinomial. Notice that it fits the form $(ax - b)^2 = a^2x^2 - 2abx + b^2$.

Let's rewrite the expression: $9x^2 - 12x + 4 = (3x - 2)^2$

Therefore, the length of each side of the square is: $3x - 2$

Part B: The area of a rectangle is given by the expression $25x^2 - 16y^2$ square units. To determine the dimensions of the rectangle, we need to factor this expression completely.

1. Recognize that the expression is a difference of squares. The difference of squares can be factored using the formula $a^2 - b^2 = (a + b)(a - b)$.

Let's apply this formula: $25x^2 - 16y^2 = (5x)^2 - (4y)^2$ $= (5x + 4y)(5x - 4y)$

Therefore, the dimensions of the rectangle are: $5x + 4y$ and $5x - 4y$