Multiply $(x-3)(4 x+2)$ using the FOIL method. Select the answer choice showing the FOIL method products.
A. $(x)(4 x)+2(x)+(-3)(4 x)+(-3)(2)$
B. $(x-3)(4 x)+(4 x)(2)$
C. $(x)(4 x+2)+(x-3)$
D. $(x-3)(4 x)+(x-3)(2)
Answer (1)
The FOIL method is applied to the expression ( x − 3 ) ( 4 x + 2 ) . The products of the First, Outer, Inner, and Last terms are calculated. The resulting expression is ( x ) ( 4 x ) + ( x ) ( 2 ) + ( − 3 ) ( 4 x ) + ( − 3 ) ( 2 ) . The correct answer choice is A. ( x ) ( 4 x ) + 2 ( x ) + ( − 3 ) ( 4 x ) + ( − 3 ) ( 2 )
Explanation
Understanding the Problem We are asked to multiply two binomials ( x − 3 ) and ( 4 x + 2 ) using the FOIL method and select the correct expression that represents the FOIL method application. The FOIL method stands for First, Outer, Inner, Last, which refers to the order in which we multiply the terms of the two binomials.
Applying the FOIL Method Applying the FOIL method to the expression ( x − 3 ) ( 4 x + 2 ) :
First: Multiply the first terms of each binomial: x × 4 x = 4 x 2 .
Outer: Multiply the outer terms of the binomials: x × 2 = 2 x .
Inner: Multiply the inner terms of the binomials: − 3 × 4 x = − 12 x .
Last: Multiply the last terms of each binomial: − 3 × 2 = − 6 .
Combining the products from each step, we get: ( x ) ( 4 x ) + ( x ) ( 2 ) + ( − 3 ) ( 4 x ) + ( − 3 ) ( 2 ) .
Identifying the Correct Answer Comparing the resulting expression with the answer choices, we see that it matches answer choice A: ( x ) ( 4 x ) + 2 ( x ) + ( − 3 ) ( 4 x ) + ( − 3 ) ( 2 ) .
Examples
The FOIL method is a fundamental technique in algebra used to expand binomial expressions. For example, if you're calculating the area of a rectangular garden where the length is (x - 3) meters and the width is (4x + 2) meters, you would use the FOIL method to find the expanded expression for the area. This method ensures that you account for all possible products when multiplying two binomials, which is crucial in various algebraic manipulations and problem-solving scenarios.
