Question
Simplify: $(9 x-7)(2 x-5)-(3 x-8)(5 x-3)$
✓
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
Estimate what part of the figures is coloured and hence find the per cent which is coloured
The area of a circle is $1381m^2$. Find its circumference.
→Simplify the following algebraic expressions by removing grouping symbols.
$x^2-\left[3 x+\left\{2 x-\left(x^2-1\right)\right\}+2\right]$
→$x^2-\left[3 x+\left\{2 x-\left(x^2-1\right)\right\}+2\right]$
Age (in years) of $6$ children of two groups are recorded as below:
→|
Age (in Years)
|
|
|
Group A
|
Group B
|
|
$7$
|
$7$
|
|
$7$
|
$9$
|
|
$9$
|
$11$
|
|
$8$
|
$12$
|
|
$10$
|
$12$
|
|
$10$
|
$12$
|
- Find the mode and range for each group.
- Find the range and mode if the two groups are combined together.
Subtract:
$-x^2-3 z$ from $5 x^2-y+z+7$
→$-x^2-3 z$ from $5 x^2-y+z+7$
Find the difference:
$4 \frac{3}{10}-1 \frac{2}{15}$
→$4 \frac{3}{10}-1 \frac{2}{15}$
Determine the integer whose product with ' $-1^{\prime}$ is
(i) 58 (ii) 0 (iii) -225
→(i) 58 (ii) 0 (iii) -225
The sum of two rational numbers is $-3$ If one of them is $\frac{-15}{6}$ find the other.
→What are rational numbers? Give examples of five positive and five negative rational numbers. Is there any rational number which is neither positive nor negative? Name it.
Write the following rational number in the standard form:
$\frac{-63}{-210}$
→$\frac{-63}{-210}$