Question

(4x - 1)(-9x + 3) + 7(13 + 5x - x2) write equivalent expression in standard form​

Answer 1

The expression (4x - 1)(-9x + 3) + 7(13 + 5x - x^2) can be expanded and simplified to the standard form by distributing, combining like terms, and simplifying to get -43x^2 + 56x + 88.

Step-by-step explanation:

To write the given expression (4x - 1)(-9x + 3) + 7(13 + 5x - x2) in standard form, we need to distribute and combine like terms.

1. First distribute in the first binomial: (4x)(-9x) + (4x)(3) + (-1)(-9x) + (-1)(3).
2. This simplifies to -36x2 + 12x + 9x - 3.
3. Now combine like terms: -36x2 + (12x + 9x) - 3 simplifies to -36x2 + 21x - 3.
4. Next, distribute the 7 into the second set of parentheses: 7(13) + 7(5x) - 7(x2).
5. This results in 91 + 35x - 7x2.
6. Add the results from steps 3 and 5: (-36x2 + 21x - 3) + (91 + 35x - 7x2)
7. Combine all like terms: -36x2 - 7x2 + 21x + 35x - 3 + 91.
8. The expression now is -43x2 + 56x + 88.

This is the standard form of the given expression which can be reordered to -43x2 + 56x + 88 = 0 for solving quadratic equations.