Question
Simplify:
$(9 x-7)(2 x-5)-(3 x-8)(5 x-3)$
$(9 x-7)(2 x-5)-(3 x-8)(5 x-3)$
✓
Answer
$(9 x-7)(2 x-5)$
$=9 x \times(2 x-5)-7(2 x-5)$
$=18 x^{(1+1)}-45 x-14 x+35$
$=18 x^2-59 x+35$
$(3 x-8)(5 x-3)$
$=3 x(5 x-3)-8(5 x-3)$
$=15 x^2-9 x-40 x+24$
$=15 x^2-49 x+24$
$\therefore(2 x-5)-(3 x-8)(5 x-3)$
$=18 x^2-59 x+35-\left(15 x^2-49 x+24\right)$
$=18 x^2-15 x^2-59 x+49 x+35-24$
$=3 x 2-10 x+11$
$=9 x \times(2 x-5)-7(2 x-5)$
$=18 x^{(1+1)}-45 x-14 x+35$
$=18 x^2-59 x+35$
$(3 x-8)(5 x-3)$
$=3 x(5 x-3)-8(5 x-3)$
$=15 x^2-9 x-40 x+24$
$=15 x^2-49 x+24$
$\therefore(2 x-5)-(3 x-8)(5 x-3)$
$=18 x^2-59 x+35-\left(15 x^2-49 x+24\right)$
$=18 x^2-15 x^2-59 x+49 x+35-24$
$=3 x 2-10 x+11$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The sum of two rational numbers is -3 If one of them is $\frac{-15}{6}$ find the other.
→Find the mode and median of the data: $13,16,12,14,19,12,14,13,14$
By using the empirical relation also find the mean.
→By using the empirical relation also find the mean.
A room is 9 m by 8 m by 6.5 m . It has one door of dimensions ( $2 m \times 1.5 m$ ) and four windows each of dimensions ( $1.5 m \times 1 m$ ). Find the cost of painting the walls at Rs 50 per $m ^2$.
→Find the median of first 10 even numbers.
Add the following rational numbers:
$-4\text{ and }\frac{1}{2}$
→$-4\text{ and }\frac{1}{2}$
Find the median of:
55, 60, 35, 51, 29, 63, 72, 91, 85, 82
55, 60, 35, 51, 29, 63, 72, 91, 85, 82
Evaluate:
$\frac{4}{9}-\frac{2}{-3}$
→$\frac{4}{9}-\frac{2}{-3}$
Add the following rational numbers:
$\frac{-2}{5}\text{ and }\frac{3}{4}$
→$\frac{-2}{5}\text{ and }\frac{3}{4}$
The heights (in cm) of 40 boys were measured and recorded as under:
Find the mean height.
| Height (in cm) | 165 | 170 | 175 | 180 |
| Number of boys | 9 | 8 | 11 | 12 |
Find the mean height.
In the figure given alongside, find:
→- $\angle\text{ACD}$
- $\angle\text{AED}$