Question

How do you simplify \[5\left( x+3 \right)\left( x+2 \right)-3\left( {{x}^{2}}+2x+1 \right)\]?

Answer 1

Hint: In this problem, we have to simplify the given expression, we can first multiply the number 5 inside the bracket and we can multiply the two factors to get an equation. We can multiply the number 3 inside its respective bracket to form another equation, we can then subtract the two equations to get another equation which is the simplified form.

Complete step by step solution:
We know that the given expression to be simplified is,
 \[5\left( x+3 \right)\left( x+2 \right)-3\left( {{x}^{2}}+2x+1 \right)\]
We can now multiply the number 5 and 3 inside the respective bracket, we get
\[\Rightarrow \left( 5x+15 \right)\left( x+2 \right)-\left( 3{{x}^{2}}+6x+3 \right)\]
We can now multiply the two factors to get an equation.
We can multiply each term in first factor to each term in the second factor, we get
\[\Rightarrow \left( 5{{x}^{2}}+10x+15x+30 \right)-\left( 3{{x}^{2}}+6x+3 \right)\]
We can remove the brackets as we have subtraction sign to subtract the two equations, we get
\[\Rightarrow 5{{x}^{2}}+10x+15x+30-3{{x}^{2}}-6x-3\]
Now we can rearrange the above step by subtracting the similar terms from the highest power to the constant,
\[\Rightarrow 5{{x}^{2}}-3{{x}^{2}}+10x-6x+30-3\]
Now we can simplify the above step, by subtracting the similar terms with the variables and the constant to get a simplified form.
\[\Rightarrow 2{{x}^{2}}+4x+27\]

Therefore, the simplified form of the given expression by adding the give two quadratic equation \[5\left( x+3 \right)\left( x+2 \right)-3\left( {{x}^{2}}+2x+1 \right)\] is \[2{{x}^{2}}+4x+27\].

Note: Students make mistakes while multiplying the two factors. We can multiply each term in the first factor to each term in the second factor. We should also concentrate on the part of subtracting the second equation by multiplying the negative sign inside the bracket to remove it.