When a variable 'x' is multiplied with another variable 'y', the algebraic expression formed is 'xy'.

$-2(3y+6)=(-2\times 3y)+(-2\times 6)$
$=-6y+(-12)$
$=-6y-12$

Steps: 1 Mark
Answer: 1 Mark
The value of the polynomial $a^3+3a^{2}b+2ab-b^2$ at  a = -2 and b = 3
$a^3+3a^{2}b+2ab-b^2$
On substituting the values of a and b in the above expression we get:
$=(-2{)}^3+3\times (-2{)}^2\times 3+2\times (-2)\times 3-3^2$
$=-8+36-12-9=7$
So, the value of the polynomial $a^3+3a^{2}b+2ab-b^2$ at $a=-2$ and $b=3$ is 7.

Simplified equation: 1 Mark
Name of expression: 1 Mark
The given equation is:
$(3x-8y+4)-(x-y)$
$=3x-8y+4-x+y$
$=2x-7y+4$
where $2x,7y$ and $4$ are the three terms.
So, the simplified equation is a trinomial.

Each part: 1.5 Marks
(i) Value of the expression for $x=-4$
$2x^2+12x+3$
$2(-4{)}^2+12(-4)+3$
$2\left(16\right)-48+3$
$32-48+3=-15$
Hence, the value of expression $2x^2+12x+3$ at $x=-4$ is lesser than 15.
(ii) As per question
$x^2$ is added to $2x^2+12x+3$ and 15 is subtracted from it
So, the final expression is:
$2x^2+12x+3+x^2-15$
$3x^2+12x-12$
On putting x = -4 in the above equation we get:
$3\times (-4{)}^2+12\times (-4)-12$
$=48-48-12$
$=-12$
 

Forming the expression: 1 Mark
Value of expression: 1 Mark
The product of two numbers, m, and n is
m$\times$n.
Three times the product is 3mn.
Adding 5 to three times the product
= 5 + 3mn
The expression formed is 5 + 3mn
The value of the product at m = 4 and n = 5
$=5+3\times 4\times 5=65$
Hence, the value of the expression if m = 4 and n = 5 is 65.

Formula: 1 Mark
Steps: 1 Mark
Answer: 1 Mark
Given that:
Two adjacent sides of a rectangle are $5x^2-3y^2$ and $x^2-2xy$.
The perimeter of a rectangle is given by:
Perimeter of a rectangle = 2 (Length + Breadth)
$=2\left[\right(5x^2-3y^2)+(x^2-2xy\left)\right]$
$=[10x^2-6y^2)+(2x^2-4xy)]$
$=12x^2-6y^2-4xy$
So, the perimeter of the rectangle is $12x^2-6y^2-4xy$.

Steps: 2 Marks
Answer: 1 Mark
Steps to be followed to decide whether the given terms are like or not are as followed:
i) Ignore the numerical coefficients.
ii) Check the variables in the terms. They must be same otherwise they are unlike terms.
iii) Next, check the powers of each variable in the terms. They should be the same and if they are not then they are not like terms.
We have to check if $x^{2}andxy$ are like terms.
The variables in both these expressions are $xandy$.
The power of $y$ is equal in both the expressions.
But the power of $x$ in the term $x^{2}y$ is 2, while in the term $xy$ it is one.
$\therefore$ The terms are not like.