Question

How do you solve the given equation with “3” terms, \[(8{r^2} + 4r + 6)(3{r^2} - 7r + 1)\]?

Answer 1

Hint:Here in this question we need, to expand the term by multiplying the given terms. Here you have to expand one bracket then multiply each every term of another bracket one by one of the first bracket then simply simplify the terms which are going to be simplified, like do some addition or subtraction and write your answer in the most simplest term.

Complete step by step solution:
For the given equation we have to expand the term and solve further.
The given equation is:
\[(8{r^2} + 4r + 6)(3{r^2} - 7r + 1)\]
Firstly we have to break the first bracket, each term of first bracket should be in multiplication with the whole next bracket and this process should be carried on as whole terms of first bracket are multiplied with the whole next bracket:
On solving we get:
\[
= (8{r^2} + 4r + 6)(3{r^2} - 7r + 1) \\
= 8{r^2}(3{r^2} - 7r + 1) + 4r(3{r^2} - 7r + 1) + 6(3{r^2} - 7r + 1) \\
= (8{r^2} \times 3{r^2}) - (8{r^2} \times 7r) + (8{r^2} \times 1) + (4r \times 3{r^2}) - (4r \times 7r) +
(4r \times 1) + (6 \times 3{r^2}) - (6 \times 7r) + (6 \times 1) \\
= 24{r^4} - 56{r^3} + 8{r^2} + 12{r^3} - 28{r^2} + 4r + 18{r^2} - 42r + 6 \\
= 24{r^4} - 44{r^3} - 2{r^2} - 38r + 6 \\
\]
This is the required expansion we need.

Additional Information: Above is the required expansion we need to go through, and the rest method is very simple and precise, you have to just open the terms and solve accordingly by multiplying with the each term of the bracket, and you will be having your result.

Note: For simplification of two brackets you need to be careful with the sign assigned to the terms, these signs either of addition or subtraction will multiply with the whole next bracket and accordingly the results should be obtained, next thing to keep in mind is the appropriate calculation needed with the variables.