Question

How do you simplify \[\left( 2x-3 \right)\left( x-7 \right)\] ?

Answer 1

Hint: In this problem we have to simplify the given factors to an equation. Here with the given factors, we can separate the first factor and subtract it with the second factor, then we can simplify by adding and subtracting the terms in order to get a quadratic equation, the simplified one must be the quadratic equation, as we have two x to be multiplied. We can also use a method FOIL to multiply two binomials.

Complete step by step answer:
We know that the given factors are,
\[\left( 2x-3 \right)\left( x-7 \right)\]
Now we can separate the first factor to be multiplied with the other, we get
\[\Rightarrow 2x\left( x-7 \right)-3\left( x-7 \right)\]
Then, we can multiply the outer terms with the inner factors in the bracket, we get
\[\begin{align}
  & \Rightarrow \left[ 2x\left( x \right)-2x\left( 7 \right) \right]-\left[ 3\left( x \right)-3\left( 7 \right) \right] \\
 & \Rightarrow 2{{x}^{2}}-14x-3x+21 \\
\end{align}\]
Now we can combine these terms, that is, we have two x terms to be added to get a simplified quadratic equation.
\[\Rightarrow 2{{x}^{2}}-17x+21\]
Therefore, the simplified equation is \[2{{x}^{2}}-17x+21\]

Note: Students make mistakes in positive and negative signs, while multiplying can be rectified.
We can use the FOIL method here, to multiply two binomials to simplify it.
We know that the given factors are,
\[\left( 2x-3 \right)\left( x-7 \right)\]
From the above factor, we can write,
F – Firsts \[\Rightarrow 2x\times x=2{{x}^{2}}\]
O – Outsides \[\Rightarrow 2x\times -7=-14x\]
I – Insides \[\Rightarrow -3\times x=-3x\]
L – Lasts \[\Rightarrow -3\times -7=21\]
Now adding these four terms we get, \[2{{x}^{2}}-17x+21\]
Therefore, the simplified equation is \[2{{x}^{2}}-17x+21\]
The FOIL method is a simpler way to multiply two binomials directly, Students make mistakes while choosing correct terms to be multiplied with and it should be concentrated.