Comparing (y-5)³ with (a-b)³,we get a = y,b = 5
(a-b)³ = a³- 3a²b + 3ab + 3ab²-b²
(y - 5)³ = (y)³ + 3(y)²(5) + 3(y)(5)² - (-5)³
= (y)³+ 3y²(5) + 3(y)(25)-125
(y - 5)³ = y³-15y² + 75y-125

Comparing it with (a + b)(a - b) we get a = 3x b = 5y
Now (a + b)(a - b) = a²-b²
(3x + 5y)(3x - 5y) = (3x)² - (5y)² (replacing a and b values)
= 3² x² - 5² y²
(3x + 5y) (3x - 5y) = 9x² - 25y²

We know, 998 can be expressed as (1000 − 2)
Now (a - b)a² - 2ab + b²
(1000 - 2)² = (1000)22(1000(2) + (2)²
= 1000000 - 4000 + 4
(998)² = 996004

The resultant expression
=3xy × (2x+3y+50)
=3xy(2x)+3xy(3y)+3xy(50)
=6x²y+9xy²+150xy

= 3x²y(2x³y³) − 3x²y(5x²y) + 3x²y(9xy)
multiplying each term of the polynomial by the monomial
= (3 × 2)(x² × x³)(y × y³)−(3 × 5)(x² × x²)(y × y) + (3 × 9)(x² × x)(y × y)
= 6x⁵y⁴−15x⁴y² + 27x3y²

(x + y)²=x²+y²+2xy
12²=x²+y²+2X14
144=x³+y²+28
x²+y²=116

\(\cfrac { { 6x }^{ 4 }yz-{ 3xy }^{ 3 }+{ 8x }^{ 2 }{ yz }^{ 4 } }{ 2xyz } =\cfrac { { 6x }^{ 4 }yz }{ 2xyz } -\cfrac { 3xy^{ 2 }z }{ 2xyz } +\cfrac { { 8x }^{ 2 }{ yz }^{ 4 } }{ 2xyz } \)
= \(\cfrac { 6 }{ 2 } { x }^{ 4-1 }{ y }^{ 1-1 }{ z }^{ 1-1 }-\cfrac { 3 }{ 2 } { x }^{ 1-1 }{ y }^{ 3-1 }z^{ 1-1 }+\cfrac { 8 }{ 2 } { x }^{ 2-1 }{ y }^{ 1-1 }{ z }^{ 4-1 }\) 
= \(3{ x }^{ 3 }{ y }^{ 0 }{ z }^{ 0 }-\cfrac { 3 }{ 2 } { x }^{ 0 }{ y }^{ 2 }{ z }^{ 0 }+{ 4xy }^{ 0 }{ z }^{ 3 }\) 
= \({ 3x }^{ 3 }-\cfrac { 3 }{ 2 } { y }^{ 2 }-4{ xz }^{ 3 }\)

(5 -x)(3 - 2x) (4 - 3x) = {(5 -x) (3 - 2x)} x (4 - 3x) [\(\therefore\) Multiplication in association]
= {5(3-2x)-x(3-2x)}X(4-3x)
= (15 - 10x - 3x + 2x²) x (4 - 3x)
= (2x²-13x+15)(4-3x)
= 2x²X(4-3x)-13x(4-3x)+15(4-3x)
= 8x³-6³-52x+39x²+60-45x
= -6x³+47x²-97x+60

We have 8p³+ q³
This can be written as = 23p³+ q³
= (2p)³+ q³
Comparing this with a³+ b^3, we get a = 2p,b = q
We know a³+ b³ = (a+b) (a²−ab+b²)
(2p)³+ q³ = (2p+q)[(2p)²−(2p)(q)+q²]
8p³+ q³ = (2p+q) [4p²−2pq+q²]

\(speed=\cfrac { distancetravelled }{ timetaken } \)
= \(\cfrac { { 4x }^{ 2 }+3{ xy }^{ 2 }+5x }{ 2x } \)

= \({ 2x }^{ 2-1 }+\cfrac { 3 }{ 2 } { y }^{ 2 }+\cfrac { 5 }{ 2 } \)
Speed = \(\left( 2x+\cfrac { 3 }{ 2 } { y }^{ 2 }+\cfrac { 5 }{ 2 } \right) \) km/hr