Question

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

Answer 1

Hint: The FOIL method is a technique used to help remember the steps required to multiply two binomials. Multiply each term in the first binomial with each term in the second binomial using Foil method as shown,
\[\left( {ax + b} \right)\left( {cx + d} \right) = ax \cdot cx + ax \cdot d + b \cdot cx + b \cdot d\].

Complete step-by-step solution:
Two binomials can be multiplied using Foil method, while multiplying the polynomial, each term of one earlier, while multiplying the polynomial, each term of one polynomial needs to be multiplied by another term of the polynomial. The foil method is just a technique of remembering the series or order of finding the product.
The FOIL method is a technique used to help remember the steps required to multiply two binomials. Remember that when you multiply two terms together you must multiply the coefficient (numbers) and add the exponents, and finally combine the like terms.
Now given expression is \[\left( {2x + 5} \right)\left( {4x - 3} \right)\],
Multiply the first terms of both the binomials that are \[2x\] from \[2x + 5\] and \[4x\] from \[4x - 3\]. The product of \[2x\] and \[4x\] i.e.,
\[2x \cdot 4x = 8{x^2}\],
Now then we will multiply the outer terms of both the binomials, the product of outer terms that are \[2x\] from \[2x + 5\] and -3 from \[4x - 3\] i.e.,
\[2x \cdot - 3 = - 6x\],
Now multiply the inner terms of the binomials. The inner terms here are 5 from \[2x + 5\] and \[4x\] from \[4x - 3\] i.e.,
\[5 \cdot 4x = 20x\],
 At last multiply the last terms in each of the two binomials, the last two terms here are 5 from \[2x + 5\] and -3 from \[4x - 3\], so the product will be i.e.,
\[5 \cdot - 3 = - 15\].
So this is can represented as,
$\Rightarrow$\[\left( {2x + 5} \right)\left( {4x - 3} \right) = 2x \cdot 4x + 2x \cdot - 3 + 5 \cdot 4x + 5 \cdot - 3\],
By simplifying we get,
$\Rightarrow$\[\left( {2x + 5} \right)\left( {4x - 3} \right) = 8{x^2} - 6x + 20x - 15\],
Now by combining the like terms we get,
$\Rightarrow$\[\left( {2x + 5} \right)\left( {4x - 3} \right) = 8{x^2} + 14x - 15\]

By Foil method we get,
\[\left( {2x + 5} \right)\left( {4x - 3} \right) = 8{x^2} + 14x - 15\].

Note: Method of foil method will be: First multiply the first terms, then the outer terms, then the inner terms and finally the last terms.
The product of two positive will be positive.
The product of two negatives will also be positive.
The product of a positive and negative will always be negative.