Question

How do you foil \[\left( 2x+5 \right)\left( 4x-3 \right)\].

Answer 1

Hint: First we should know what it means to foil an expression. For an expression of the form \[(a+b)(c+d)\]. FOIL involves carrying out the below operations in the following order:
Operation 1: product of the First terms – a product of the first terms of two brackets \[ac\].
Operation 2: product of the Outside terms – the product of the first term of the first bracket and the second term of the second bracket \[ad\].
Operation 3: product of Inside terms – a product of the second term of the first bracket and first term of the second bracket \[bc\].
Operation 4: product of Last terms – the product of the second terms of two brackets \[bd\].
And at last, adding the results of the above four operations.

Complete step by step solution:
We are given the expression \[\left( 2x+5 \right)\left( 4x-3 \right)\], we are asked to FOIL the given expression.
To foil an expression, we have to carry out some operations, we will do them for the given expression

The first operation is to the product of the first terms of two brackets,
\[\Rightarrow 2x\times 4x=8{{x}^{2}}\]

The second operation is the product of the first term of the first bracket and the second term of the second bracket
\[\Rightarrow 2x\times -3=-6x\]

The third operation is the product of the second term of the first bracket and the first term of the second bracket
\[\Rightarrow 4x\times 5=20x\]
The fourth operation is the product of the second terms of two brackets
\[\Rightarrow -3\times 5=-15\]

Finally, we have to add the results of the above four operations, by doing this we get
\[\begin{align}
  & 8{{x}^{2}}-6x+20x-15 \\
 & \Rightarrow 8{{x}^{2}}+14x-15 \\
\end{align}\]


Note: This expression of the form \[\left( a+b \right)\left( c+d \right)\]. We know that this expression is expanded by multiplying each term of the first bracket with each term of the second bracket and then adding their products. Algebraically it is expressed as, \[\left(a+b \right)\left( c+d \right)=ac+ad+bc+bd\]