(i) 30 abcxyz   
(ii) m³n³p³   
(iii) 64q⁶

-30 apqx⁶

Here, Length = 3x² - 2
Breadth = 2x + 5
∴ Area= (Length)\(\times\)(Breadth
 = (3x²- 2)\(\times\)(2x + 5)
=  3x²(2x + 5) + (-2)(2x + 5)
= (3x²\(\times\)2x) + (5\(\times\)3x²) + [(-2)\(\times\)2x + (-2)\(\times\)5]
= 6x³+ 15x²+ (-4x) + (-10)
= 6x³ + 15x² - 4x -10
Thus, the required area of the rectangle is 6x³ + 15x²- 4x - 10 sq. units

We have
(x + a)(x + b) = x²+ (a + b)x + ab
Puting a = 2, b = 3 and x = 4, we have
LHS = (x + a)(x + b)
= (4 + 2)(4 + 3)
= 6\(\times\)7 = 42
RHS = x²+ (a + b)x + ab
 = (4)² + (2 + 3)4 + (2\(\times\)3)
= 16 + 5\(\times\)4 + 6
= 16 + 20 + 6 = 42
i.e., LHS = RHS
Thus, the given identity is true for the given values

LHS= (a - b)(a + b) + (b - c)(b + c) + (c - a)(c + a)
= (a²-b²) + (b²-c²) + (c²-a²)
= a²-b² + b²-c² +c²-a²
= a²- a² + b² - b² + c² - c² = 0 = RHS
Since, LHS = RHS
∴ (a - b)(a + b) + (b - c)(b + c) + (c - a)(c + a) = 0

LHS=(4pq + 3q)² - (4pq - 3q)²
= [(4pq)² + 2(4pq)(3q) + (3q)²] - [(4pq)² - 2(4pq)(3q) + (3q)²]
= 16p²q² + 24pq² + 9q²-[16p²q²-24pq²+ 9q²]
=  16p²q² + 24pq² + 9q²-16p²q²-24pq²- 9q²
= (16 - 16)p²q² + (24 + 24)pq² + (9 - 9)q²
= (0)p²q² + 48pq² + (0)q² = 48pq² = RHS
Since, LHS = RHS
∴ (4pq + 3q)² - (4pq - 3q)²  = 48pq²

For subtraction, write the like terms one below the other, we get
5xy - 2yz - 2zx + 10xyz
+ 3xy + 5y z- 7zx
(-)      (-)  (+)
_______________________
2xy-7yz + 5zx + 10xyz
_______________________
Thus, the required answer is 2xy - 7yz + 5zx + 10xyz

=[(2.5p)² - 2(2.5p)(1.5q) + (1.5q)²] - [(1.5p)² - 2(1.5p)(2.5q) + (2.5q)²]
= 6.25p² - 7.5pq + 2.25q² - [2.25p² - 7.5pq + 6.25q²]
= 6.25p² - 7.5pq + 2.25q² - 2.25p² + 7.5pq - 6.25q²
= (6.25 - 2.25)p² + (-7.5+7.5)pq + (2.25-6.25)q²
= 4p² + 0(pq) - 4q² = 4p² -4q²

[(4m)² + 2(4m)(5n) + (5n)²] + [(5m)² + 2(5m)(4n) +(4n)²]
= 16m² + 40mn + 25n² + 25m² + 40mn + 16n²
=  (16 + 25)m²+ (40 + 40)mn + (25 + 16​​​​​)²
= 41m² + 80mn + 41n²

(7m - 8n)² + (7m + 8n)²
= [(7m)² - 2(7m)(8n) + (8n)²] + [(7m)² + 2(7m)(8n) + (8n)²]
and (a-b)²= a² -2ab+b²
= (49m² -112mn + 64n²)+(49m² +112mn + 64n²)
= 49m² -112mn + 64n² + 49m² +112mn + 64n²
= 98m² + 128n²

First expression = 3l(l - 4m + 5n)
= (3l) x (l) - (3l) x (4m) + (3l) x (5n)
= 3l² -12lm + 15ln
Second expression = 4l(10n - 3m + 2l)
= (4l)x (I0n) - (4l) x (3m) + (4l) x (2l)
= 40ln -12lm + 8l²
On subtracting first expression from second expression, we get
40ln -12lm + 8l²
15ln - 12lm + 3l²
(-)      (+)     (-)
___________________
25ln + 0 + 5l²
___________________
= 25ln + 5l²

First expression = 2x(z - x - y)
= (2x) x z - (2x) x (x) - (2x) xy
= 2xz - 2x² - 2xy
Second expression = 2y(z - y - x)
= (2y)x(z)-(2y) x (y)-(2y)x(x)
= 2yz - 2y² - 2yx
On adding above expressions, we get
2xz - 2x² - 2xy
+              -2yx + 2yz - 2y²
_________________________
2xz - 2x² - 4xy + 2yz - 2y²
__________________________

4b+2

-a²-3b²

For subtraction, write the like terms one below the other, we get
12a -9ab +5b -3
+4a - 7ab + 3b + 12
(-)     (+)     (-)    (-)
_________________
8a - 2ab + 2b -15
_________________
Thus, the required answer is 8a - 2ab + 2b - 15.