The required expression is obtained by subtracting 2b²-a² from b²-2a²
b² - 2a² - (2b² - a²) = b² - 2a² + (-2b² + a²)
= b² - 2a² - 2b² + a²
= (1 - 2)b² + (-2 + 1)a² = -b² - a²
So -b² - a² must be added

The required expression can be obtained as follows
= 2x³ - 2x² + 3x - 5 - (2x³ + 7x²x  +7)
= 2x³ - 2x² + 3x + 5 + (-2x³ - 7x² + 2x - 7)
= 2x³ - 2x² + 3x + 5 - 2x³ - 7x² + 2x - 7
= (2 - 2)x³ + (-2 - 7)x² + (3 + 2)x + (5 - 7)
= 0x³ + (- 9x²) + 5x - 2
= - 9x² + 5x - 2
\(\therefore\) 2x³- 2x² + 3x + 5 is greater than 2x ³+ 7x² - 2x + 7 by -9x² + 5x - 2

Given:
A = 2a² - 4b-1; B = 5a² + 3b - 8 and C = 2a² + 9b + 3
A + B + C = (2a² - 4b - 1) - (5a² + 3b-  8)+(2a² - 9b + 3)
= 2a² - 4b - 1 + (5a² - 3b + 8) + 2a - 9b + 3
= 2a²- 4b - 15a ²- 3b + 8 + 2a² - 9b + 3
= 2a² - 5a² + 2a² - 4b - 3b - 9b -1 + 8 + 3
= (2 - 5 + 2)a² - 4b - 3b - 9b - 1 + 8 + 3
= -a² - 16b + 10

The numbers are natural and consecutive. Let the numbers be x and x + 1.
Given that,
x + (x + 1) = 75
2x + 1 = 75
2x + 1 − 1 = 75 − 1 [Subtract 1 on both sides]
2x + 0 = 74
\(\frac {2x }{2 } =\frac { 74 }{ 2 } \) [Divide 2 at both sides]
x = 37 and x + 1 = 38
Therefore, the required numbers are 37 and 38.

3x - 5 - x + 9 = 3(3) - 5 - 3 + 9
= 9 - 5 - 3 + 9 =18 - 8 =10

Perimeter = (y - 2) + (y - 2) + (y - 2) + (y -2)
= y - 2 + y - 2 + y - 2 + y - 2 = 4y - 8
Perimeter of the square = 4y- 8units.

Equilateral triangle has three sides equal.
Perimeter = Sum of three sides
= (3x - 4) + (3x - 4) + (3x - 4) = 3x - 4 + 3x -4 + 3x - 4
=(3 + 3 + 3)x +  [(-4) + (-4) + (-4)] = 9x + (-12) = 9x - 12
\(\therefore\) Perimeter = 9x - 12 units

i) (3x − 4y + z) + (2x − z + 3y)
= (3x + 2x) + ( −4y + 3y) + (z − z)
= (3 + 2)x + ( −4 + 3)y + (1 − 1)z
= 5x − 1y + 0z
= 5x − y.

ii) (4x + 3y) − (2x − 5y)
= (4x + 3y) + ( −2x + 5y)
= (4x − 2x) + (3y + 5y)
= (4 − 2)x + (3 + 5)y
= 2x + 8y.

In the given algebraic expression, x,y,z are the variables.
Let us group the like terms.
100x + 99y − 98z + 10x + 10y + 10z − x − y + z
= (100x + 10x − x) + (99y + 10y − y) + ( −98z + 10z + z)
= (100 + 10 − 1)x + (99 + 10 − 1)y + ( −98 + 10 + 1)z
= (110 − 1)x + (109 − 1)y + ( −98 + 11)z
= 109x + 108y + ( −87)z
= 109x + 108y − 87z.