Question

Multiply $(3x - 3y)$ and $(4y - 3x)$.

Answer 1

Hint: First, we will see what multiplication is, Multiplicand refers to the number multiplied. The multiplier is the number that refers to the number which multiplies the first number.
Here in this problem, we have to multiply two values with different variables like the first value is $(3x - 3y)$ and the second value is $(4y - 3x)$
By the multiplication operation, we solve this further below.

Complete step by step answer:
For the given that, we have to multiply them $(3x - 3y)$ and $(4y - 3x)$which means, by the multiplication, we can write the values as $(3x - 3y) \times (4y - 3x)$; where $ \times $ is the representation of the multiplication.
First, take the two values first terms which are $3x \times 4y$ and multiply this we get, $12xy$.
Similarly, take the two values second terms which is $ - 3y \times - 3x$ and multiplying this we get, $9xy$
Now for the first value in the first term and the second value in the second term we get, $3x \times - 3x = - 9{x^2}$
Finlay another term second value in one and the first value in two we get, $ - 3y \times 4y = - 12{y^2}$
Now approaching further with all the values, we get, $(3x - 3y) \times (4y - 3x) \Rightarrow 12xy + 9xy - 9{x^2} - 12{y^2}$
Equating the common terms we get, $12xy + 9xy - 9{x^2} - 12{y^2} \Rightarrow - 9{x^2} - 12{y^2} + 21xy$
Hence which is the multiplication of $ - 9{x^2} - 12{y^2} + 21xy$is $(3x - 3y)$ and $(4y - 3x)$

Additional information:
The addition is the sum of two or more than two numbers, or values, or variables, and in addition, if we sum the two or more numbers a new frame of the number will be found.
If the question is about the addition of the two values, then we get, $(3x - 3y) + (4y - 3x) \Rightarrow 3x - 3x + 4y - 3y \Rightarrow y$ cancel out the common terms.
Subtraction operation, which is the minus of two or more than two numbers or values but here comes with the condition that in subtraction the greater number sign will stay constant example$2 - 3 = - 1$ .
If the question is about subtraction of the two values, then we get, $(3x - 3y) - (4y - 3x) \Rightarrow - 7y + 6x$cancel out the common terms.

Note: Have a look at an example; while multiplying $5 \times 7$ the number $5$ is called the multiplicand and the number $7$ is called the multiplier. Thus $3.87$ is the multiplicand and $1.25$ is called the multiplier.
For division, like $x \times y = z$ is multiplication thus the division sees as $x = \dfrac{z}{y}$. We usually need to memorize the multiplication tables in childhood so it will help to do maths.