Multiply $(5 x-4)(x+y)$
a. $5 x^2+5 y-4 x-4 y$
b. $5 x^2+5 x y-4 x-4 y$
c. $5 x-4 x y-y$
d. $5 x+x y-4 x-4 y$
Answer (2)
Multiply the first terms: 5 x × x = 5 x 2 .
Multiply the outer terms: 5 x × y = 5 x y .
Multiply the inner terms: − 4 × x = − 4 x .
Multiply the last terms: − 4 × y = − 4 y .
Combine the terms: 5 x 2 + 5 x y − 4 x − 4 y . The answer is 5 x 2 + 5 x y − 4 x − 4 y
Explanation
Understanding the Problem We are given the expression ( 5 x − 4 ) ( x + y ) and asked to multiply it out. This involves using the distributive property (often remembered by the acronym FOIL: First, Outer, Inner, Last) to expand the product of two binomials.
Multiplying First Terms First, we multiply the 'First' terms: 5 x × x = 5 x 2 .
Multiplying Outer Terms Next, we multiply the 'Outer' terms: 5 x × y = 5 x y .
Multiplying Inner Terms Then, we multiply the 'Inner' terms: − 4 × x = − 4 x .
Multiplying Last Terms Finally, we multiply the 'Last' terms: − 4 × y = − 4 y .
Combining Terms Now, we combine all the terms we found: 5 x 2 + 5 x y − 4 x − 4 y .
Selecting the Correct Option Comparing our result 5 x 2 + 5 x y − 4 x − 4 y with the given options, we see that it matches option b.
Final Answer Therefore, the correct answer is 5 x 2 + 5 x y − 4 x − 4 y .
Examples
Understanding how to multiply binomials is useful in many areas, such as calculating areas of rectangles with variable side lengths. For example, if you have a garden whose length is ( 5 x − 4 ) meters and width is ( x + y ) meters, multiplying these binomials gives you the area of the garden: 5 x 2 + 5 x y − 4 x − 4 y square meters. This skill is also essential in more advanced math topics like calculus and algebra.
To multiply ( 5 x − 4 ) ( x + y ) , we use the distributive property to get 5 x 2 + 5 x y − 4 x − 4 y . The correct answer is option b . Each step involves multiplying corresponding terms from each binomial and then combining the results.
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