Question

How do you simplify $\dfrac{1}{3}(21m + 27)?$

Answer 1

Hint: As we know that to multiply means to increase in number especially greatly or in multiples. We know that the standard form of any quadratic expression is $a{x^2} + bx + c$. Here in this question we have to find the product of polynomials, we just multiply each term of the first polynomial by each term of the second polynomial and then simplify by combining terms like adding coefficients, and then combine the constants. We will simply use the distributive property to solve this.

Complete step-by-step solution:
Here we have $\dfrac{1}{3}(21m + 27)$, we will now expand the expression by using the distributive property. We must ensure that each term in the second bracket is multiplied by each term in the first bracket. This can be done as follows: $\dfrac{1}{3}(21m + 27) = \dfrac{1}{3} \times 21m + \dfrac{1}{3} \times 27$.
Now by multiplying each term of the above expression we get: $7m + 9$
As we know that the standard form of expression is of the form $a{x^2} + bx + c$.
Hence the product and of the required expression is $7m + 9$.

Note: We should note that while solving this kind of question we need to expand the term with the help of distributive property. Also we should be careful while adding or subtracting with the negative and positive signs. The distributive property says that $a \times (b + c) = a \times b + a \times c$. There are distributive properties of different types of operations i.e. for multiplication, addition, subtraction. It simply states that multiplication distributes over addition. We know that the standard form means writing the expression starting with the term which has the highest power of variable.