Explanation:
To convert expression a into expression b, we need to factorize it. We can do this by finding two numbers whose product is equal to the product of the coefficients of the first and last terms (1.5 x -584 = -876) and whose sum is equal to the coefficient of the middle term (12.5).
Let's break down -876 into its factors:
-876 = -4 x 3 x 73
We can see that 36 is one of the possible pairs of numbers whose product is equal to -876. We can also see that -24 and 36.5 are two numbers whose sum is equal to 12.5.
So, we can write expression a as:
1.5n² + 12.5n - 584
= 1.5n² - 24n + 36.5n - 584 (by splitting 12.5n as -24n + 36.5n)
= 1.5n² - 24n + 36.5n - 36 x 73 (by adding and subtracting 36 x 73)
= 1.5n² - 24n + 36.5n - 2628
Therefore, expression a can be simplified to expression b by factoring it