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Given, binomial is 5x²y² + 15xy²
So, terms are 5x²y² and 15xy².
Hence, factors of 5X²y² is 5 x x x x x y x y
and factors of 15xy² is 15 x x x y x y
or 3 x 5 x x x y x y.

We first find the sum of 3x - y + 11 and  -y - 11
\(3xy-y+11\\\quad\ \ -y-11\\ \_\_\_\_\_\_\_\_\_\_\_\\\quad 3x-2y\\\_\_\_\_\_\_\_\_\_\_\_\)
Now, we have to subtract 3x - y - 11 from the sum 3x - 2y
\(3x-2y\\3x-y-11\\-\ +\ \ \ +\\ \_\_\_\_\_\_\_\_\_\_\_\\0-y\ \ \ \ +11\\\_\_\_\_\_\_\_\_\_\_\_\)
Hence, the Required answer - y + 11

We have, ab - 4a, 4b - ab, 4a - 4b 
\(\therefore\) Required sum = ab - 4a + 4b - ab + 4a - 4b
= ab - ab - 4a + 4a + 4b - 4b [rearranging terms]
= ab(1 - 1) + a(-4 + 4) + b(4 - 4)
= ab X 0 + a X 0 + b(0)= 0 + 0 + 0 = 0

In 8y + 3x², the terms are 8y and 3x²

The term 8 y is formed by multiplying the variable y by B. The term 3x² is formed by first multiplying the variable x with itself to get x² and then multiplying x² by 3. 

If A= 3x²- 4x+ 1, B= 5x² + 3x- B,C= 4x² - 7x+ 3. Find the value of A + B - C
Then; \(\begin{matrix} A+B=3x^2-4x+1\\\quad \quad \quad\ \ \ \ 5x^2+3x-8\\ \quad \quad \quad \quad \quad\_\_\_\_\_\_\_\_\_\_\_\_ \\ \quad\ \ \ \ \ \ \ \ \ \ \ 8x^2-x-7\\ \quad\quad\quad\quad\quad\_\_\_\_\_\_\_\_\_\_\_\_ \end{matrix}\) \(\Rightarrow\) \(\begin{matrix} (A+B)-C=8x^2-x-7\\\quad \quad \quad\ \ \ \ 4x^2-7x+3\\\quad \quad -\ \ \ +\ \ \quad - \\ \quad \quad \quad \quad \quad\_\_\_\_\_\_\_\_\_\_\_\_ \\ \quad\ \ \ \ \ \ \ \ \ \ \ 4x^2+6x-10\\ \quad\quad\quad\quad\quad\_\_\_\_\_\_\_\_\_\_\_\_ \end{matrix}\)  [change the sign and then add]

Yes

Expression tmn is a monomial because it contains 1 term 7mn.

In the expression 0.1y+ 0.01y², terms with variables are 0.1yand 0.01y². So, their numerical coefficients are 0.1 and 0.01, respectively.

In the expression -4x + 5y, terms are -4x, 5y and factors of -4x are -4, x and factors of 5yare 5, y.

As per the gillen information, taxi service charges
Rs. 8 per km and fixed charge of' Rs. 50.
If taxi is hired for x km.
Then, algebraic expression for the situation is
8 x x + 50
\(\therefore\) 8x + 50 is the required expression.

Required expression is
2x³ - 3x²y + 2xy² + 3y³ - (x³ - 2x²y + 3xy² + 4y³)
= 2x³ -3x²y + 2xy² + 3y³ - x³ + 2x²y - 3xy² - 4y³
= 2x³ - x³ - 3x²y + 2x²y + 2xy² -3xy² + 3y³ - 4y³
= x³ - x²Y - xy² - y³
So, if we subtract x³ - x²y xy² - y³ from
2x³ - 3x²y + 2xy²+ 3y³, then we get
x³ -2x²y + 3xy² + 4y³