Multiply the expression\[\left( x+3 \right)\left( x-7 \right)\]?

Hint: In this problem, we have to multiply the given factors to get an equation. We can multiply those factors using the distributive property where the distributive property is \[a\left( b+c \right)=ab+ac\]. We can substitute the values for a, b and c from the question to find the multiplication of the given factors.

Complete step-by-step solution:
We know that the given factors to be multiplied are,
\[\left( x+3 \right)\left( x-7 \right)\]
Now we can use the distributive property to multiply the given two factors.
We know that the distributive property is,
\[b\left( a+c \right)=ba+bc\]
 We can now take, \[b=\left( x-7 \right),a=x,c=3\] and substitute in the above formula, we get
\[\Rightarrow x\left( x-7 \right)+3\left( x-7 \right)\]
Now, we can multiply the terms outside the brackets to the terms inside the brackets, we get
\[\Rightarrow {{x}^{2}}-7x+3x-21\]
Now we can subtract the terms with x, we get
\[\Rightarrow {{x}^{2}}-4x-21\]
Therefore, by multiplying \[\left( x+3 \right)\left( x-7 \right)\] we get \[{{x}^{2}}-4x-21\].

Note: We can also multiply the factors in the FOIL method to find the solution.
We know that the given factors to be multiplied are,
\[\left( x+3 \right)\left( x-7 \right)\]
We know that the term FOIL means Firsts Outsides Insides Lasts. We can apply this on the above factors we get,
Firsts \[x\times x\Rightarrow {{x}^{2}}\]
Outsides \[x\times -7\Rightarrow -7x\]
Insides \[3\times x\Rightarrow 3x\]
Lasts \[3\times -7\Rightarrow -21\]
Now we can add the above terms, we get
\[\Rightarrow {{x}^{2}}-7x+3x-21\]
Now we can subtract the terms with x, we get
\[\Rightarrow {{x}^{2}}-4x-21\]
Therefore, by multiplying the factors \[\left( x+3 \right)\left( x-7 \right)\] we get \[{{x}^{2}}-4x-21\].
Students make mistakes in taking the correct terms for the FOIL method, which should be concentrated. We should know the multiplication table to solve these types of problems.