Question

(х-5 1/7)*(8 2/3-х).

Answer 1

Ответ:

Пошаговое объяснение:

(х-5 1/7)*(8 2/3-х) = (x-36/7)(26/3-x) = 26/3x-x^2-36/7*26/3 + 36/7x =

= -x^2 + 26/3x+36/7x - (36*26)/(7*3) = -x^2 +290/21x - 312/7 =

= -x^2 + 13 17/21x - 44 4/7.

Answer 2

To multiply the two expressions $(x - 5 \frac{1}{7})$ and $(8 \frac{2}{3} - x)$, you can use the distributive property or the FOIL method (First, Outer, Inner, Last). Here's how you can do it step by step:

Step 1: Expand $(x - 5 \frac{1}{7})$ and $(8 \frac{2}{3} - x)$:

$(x - 5 \frac{1}{7}) = x - \frac{36}{7}$ $(8 \frac{2}{3} - x) = \frac{26}{3} - x$

Step 2: Multiply the two expanded expressions:

$(x - \frac{36}{7}) \cdot (\frac{26}{3} - x)$

Step 3: Use the FOIL method to multiply the expressions:

FOIL stands for First, Outer, Inner, Last. So you multiply the corresponding terms in each expression.

First: $(x \cdot \frac{26}{3}) = \frac{26x}{3}$ Outer: $(x \cdot (-x)) = -x^2$ Inner: $-\frac{36}{7} \cdot \frac{26}{3} = -\frac{936}{21}$ Last: $-\frac{36}{7} \cdot (-x) = \frac{36x}{7}$

Step 4: Combine the results from the FOIL method:

$\frac{26x}{3} - x^2 - \frac{936}{21} + \frac{36x}{7}$

Step 5: Simplify the expression by finding a common denominator for the fractions:

To add fractions, you need a common denominator. The least common multiple (LCM) of 3 and 7 is 21. So, rewrite the fractions with a common denominator of 21:

$\frac{26x}{3} - x^2 - \frac{936}{21} + \frac{36x}{7} = \frac{182x}{21} - x^2 - \frac{936}{21} + \frac{108x}{21}$

Step 6: Add and subtract the fractions with the common denominator:

$\frac{182x - 936 + 108x}{21} - x^2$

Step 7: Combine like terms in the numerator:

$\frac{290x - 936}{21} - x^2$

Now, you have the simplified expression:

$\frac{290x - 936}{21} - x^2$

This is the result of multiplying $(x - 5 \frac{1}{7})$ and $(8 \frac{2}{3} - x)$.