Question

Which of the following is an equivalent form of ( 1.5 x − 2.4 )² − ( 5.2 x²− 6.4 )?

A. − 2.2 x² + 1.6
B. − 2.2 x² + 11.2
C.− 2.95 x² − 7.2x + 12.16
D. − 2.95 x² − 7.2x + 0.64

Answer 1

The equivalent form of the expression ( 1.5 x − 2.4 )² − ( 5.2 x²− 6.4 ) is − 2.95 x² − 7.2x + 12.16, corresponding to option C.

Step-by-step explanation:

To find an equivalent form of the expression (1.5x − 2.4)² − (5.2x² − 6.4), we need to expand the squared term and then subtract the second expression from it.

First, let's expand (1.5x − 2.4)² using the FOIL method (First, Outer, Inner, Last):

1. (1.5x)² = 2.25x²
2. 2(1.5x)(-2.4) = -7.2x
3. (-2.4)² = 5.76

So the expansion of (1.5x − 2.4)² is 2.25x² − 7.2x + 5.76.

Now, let's subtract (5.2x² − 6.4) from that:

1. (2.25x² − 7.2x + 5.76) − 5.2x² = -2.95x² − 7.2x + 5.76
2. (-2.95x² − 7.2x + 5.76) + 6.4 = -2.95x² − 7.2x + 12.16

To find an equivalent form of (1.5x - 2.4)² - (5.2x² - 6.4), we need to simplify the given expression.

First, let's expand the square of (1.5x - 2.4):

(1.5x - 2.4)² = (1.5x)² - 2(1.5x)(2.4) + (2.4)² = 2.25x² - 7.2x + 5.76

Next, expand the square of (5.2x² - 6.4):

(5.2x² - 6.4)² = (5.2x²)² - 2(5.2x²)(6.4) + (6.4)² = 27.04x⁴ - 83.2x² + 40.96

Now, substitute these expanded expressions back into the original expression:

(1.5x - 2.4)² - (5.2x² - 6.4) = (2.25x² - 7.2x + 5.76) - (27.04x⁴ - 83.2x² + 40.96) = -27.04x⁴ + 84.45x² - 7.2x - 35.2

The equivalent form is therefore -2.95x² - 7.2x + 12.16, which corresponds to option C.