Expression x + y - xy is a trinomial because it contains 3 unlike terms x, y and -xy

The number z multiplied by itself = z X z = z².

We know that sum of numbers x and y is (x + y). Then,
one half of the sum = \(\frac { 1 }{ 2 } (x+y)\)

Subtraction of z from y = y - z

In 4x² - 5x, first obtain x² by multiplying the variable x by itself and then multiply x² by 4 to get 4x². From 4x², subtract the product of 5 and x, to get the expression 4x² - 5x.

We have -7mn+ 5, 12mn+ 2, 9mn- 8, -2mn- 3
\(\therefore\)  required sum
= - Zmn + 5 + 12mn + 2 + 9mn - 8 - 2mn - 3
= - tmn + 12mn + 9mn - 2mn + 5 + 2 - 8 - 3 [rearranging terms)
= mn (-7 + 12 + 9 - 2) + 7 -11
= mn (21- 9) - 4 = 12mn - 4

We have, t - 8tz, 3tz - z, z - t
\(\therefore\) Required sum = t - 8tz + 3tz - z + z - t
= t - t - 8tz + 3tz - z + z  [rearranging terms)
= t(1 - 1)+ tz( -8 + 3) + z( -1 + 1)
= t X 0 + tz( -5) + z X 0
= 0 - 5tz + 0 = - 5tz

Like terms are 10pq, -7qp and 78qp (have same algebraic factors p, q); 7P and 2405 p (have same algebraic factor p); 8q and -100q(have same algebraic factor q); - P² q² and 12q²P² (have same algebraic factors p, p, q, 1); -23 and 41 (both are constants); -5p² and 701p² (have same algebraic factors p, p); 13p² q, qp² (have same algebraic factors p, p, q).

Given expressions and their type are given below

We know that, the numerical factor of a term is said to be the numerical coefficient or simply the coefficient of the same term. So, the terms and corresponding coefficients are given below:

2x² y, the only term is 2x² y

Here, first multiply the variable x with itself to obtain x². Then, multiply x² by the variable y to get x²y. Finally, multiply X² y by the constant 2 to obtain 2x² y.

xy² Z, 2xy² Z, y² xz, 3xzy²

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\(\left( x-\frac { 1 }{ 2 } z \right) \)