a²b + b² - 2a² - 7ab

xy² Z, 2xy² Z, y² xz, 3xzy²

-2b

29

Given, =2x + 3,  = \(\frac { 3 }{ 2 } \) + 7 and  = x -3
i) = 2[2x6+3]+\(\frac { 3 }{ 2 } \)x 3+7 - (1-3)
= 2 x 15 +\(\frac { 9 }{ 2 } \) + 7 + 2=30 + \(\frac { 9 }{ 2 } \) + 9
= 39 + \(\frac { 9 }{ 2 } \) = \(\frac { 78+9 }{ 2 } =\frac { 87 }{ 2 } \)
ii) 
\(\frac { 1 }{ 2 } \left[ \frac { 3 }{ 2 } \times 2+7 \right] +[8-3]-3\left[ 2\times 0+3 \right] \)
\(\frac { 1 }{ 2 } \)[10] +5-9 = 5 + 5 -9 = 1

The total number of red sticks = 18 and the total number of blue sticks = 6

So, expression for the total length of sticks
= 18r + 6b = 6(3r + b)

Given, amount given to Rohan by his mother = Rs 3xy²
Amount given to Rohan by his father = Rs 5( xy² + 2)
Total amount spent by Rohan =Rs 10 - 3xy²
:. Money left with Rohan
= 3xy² + 5(xy² + 2) - (10 - 3xy²)
= 3xy² + 5xy² + 10 -10 + 3xy²
= 3xy² + 5xy² + 3xy² + 10 -10 = Rs.11 xy²

Arjun bought a rectangular plot with length x and breadth y.
Now, area of rectangular plot = Length x Breadth =x x y=xy
If the triangular part with base y and height z is sold.
So, area of triangular part = \(\frac { 1 }{ 2 } \times y\times z=\frac { 1 }{ 2 } yz\)
\(\therefore\) Area of the remaining part of the plot
= Area of rectangular plot - Area of triangular plot
=xy - \(\frac { 1 }{ 2 } \)yz=y\(\left( x-\frac { 1 }{ 2 } z \right) \)

Required expression is
0 -(99x³ - 33x² -13x - 41)
0- 99x³ + 33x² +13x + 41
- 99x³ + 33x² +13x + 41
So, if we add - 99x3 + 33x2 + 13x + 41 to
99x³ - 33x² -13x - 41, then the sum is zero

Required expression is
y⁴ -12y² + Y + 14 -(17y³ + 34y² - 51y + 68)
= y⁴ -12y² + Y + 14 -17y³ - 34y² + 51y - 68
= y⁴ -12y² - 34y² + Y + 51y+ 14 - 68 -17y³
= y⁴ - 46y² + 52y - 54 -17 y³
= y⁴ -17y³ - 46y² + 52y - 54
So, y⁴ -12y² + Y + 14is y⁴ -17y³ - 46y² + 52y- 54
greater than 17y³ + 34y² - 51y + 68.

Required expression is
-7mn + 2m² + 3n2 -(m² +2mn + n²)
= - 7mn + 2m² + 3n2 -m²- 2mn - n2
= - 7mn - 2mn + 2m² - m² + 3n² -n²
= - 9mn + m2 + 2n2
So, if we subtract m2 + 2n2 - 9 mn from
- 7mn + 2m² + 3n², then we get m² + 2mn + n².

Required expression is
x³ + y³ -(x³ + 3x²y + 3xy² + y³)
= x³ + y³ - x³ -3x² Y -3xy² -y³
=x³ -x³ + y³ -y³ -3x²y-3xy²
= - 3x²y - 3xy²
So if we add - 3x²y - 3xy²in
x³ + 3x²y + 3xy² +y³, we get x³ +y³