Question

How do you simplify $ \left( 3x+5 \right)\left( 2x-3 \right) $ ?

Answer 1

Hint: From the given question it has been asked to simplify $ \left( 3x+5 \right)\left( 2x-3 \right) $. We can clearly observe that the given question is nothing but the product of two linear expressions. We can do the product of the above given two linear expressions by the below-shown process.

Complete step by step answer:
From the question, it has been given that $ \left( 3x+5 \right)\left( 2x-3 \right) $
First of all, we have to multiply the second group with the first term in the first group.
By multiplying the second group with the first term in the first group, we get
 $ 3x\left( 2x \right)=6{{x}^{2}} $
 $ \Rightarrow 3x\left( -3 \right)=-9x $
Now, we have to multiply the second group with the second term in the first group.
By multiplying the second group with the second term in the first group, we get
 $ 5\left( 2x \right)=10x $
 $ \Rightarrow 5\left( -3 \right)=-15 $
Now, we have to add all terms we got by multiplying the terms of the first group with the second group, and then we will get the simplified expression.
By adding the terms which we got by multiplying the terms of first group with the second group, we get the below expression,
 $ 6{{x}^{2}}-9x+10x-15 $
 $ \Rightarrow 6{{x}^{2}}+x-15 $
Hence, the simplified expression of the given question $ \left( 3x+5 \right)\left( 2x-3 \right) $ is $ 6{{x}^{2}}+x-15 $
Therefore $ \left( 3x+5 \right)\left( 2x-3 \right)=6{{x}^{2}}+x-15 $
Hence, the given question is simplified.

Note:
We should be well known about the linear expressions and their properties. We should be well aware of the multiplication of the two linear expressions. We should be very careful while doing the calculation of the given question, especially in this type of question; a single sign change can change the whole problem. So we should be careful while adding the all terms. Similarly we can simplify $ \left( x+2 \right)\left( x+3 \right)={{x}^{2}}+5x+6 $ .