Which expression is equivalent to $-28xy + 35y$?
A. $7y(-4xy + 5y)$
B. $7x(-4x + 5y)$
C. $7x(-4y + 5y)$
D. $7y(-4x + 5)$
Answer (1)
To find an equivalent expression, we factor the given expression − 28 x y + 35 y .
Find the greatest common factor (GCF) of the terms, which is 7 y .
Factor out 7 y from the expression: − 28 x y + 35 y = 7 y ( − 4 x + 5 ) .
Compare the factored expression with the given options.
The equivalent expression is 7 y ( − 4 x + 5 ) .
Explanation
Understanding the problem We are asked to find an expression equivalent to − 28 x y + 35 y from the given options. To do this, we will factor the given expression and then compare it to the options.
Finding the Greatest Common Factor The given expression is − 28 x y + 35 y . We need to factor this expression. The greatest common factor (GCF) of the terms − 28 x y and 35 y is 7 y .
Factoring the expression Now, we factor out 7 y from the expression: − 28 x y + 35 y = 7 y ( − 4 x + 5 ) So, the factored expression is 7 y ( − 4 x + 5 ) .
Comparing with the options Now, we compare the factored expression 7 y ( − 4 x + 5 ) with the given options:
7 y ( − 4 x y + 5 y )
7 x ( − 4 x + 5 y )
7 x ( − 4 y + 5 y )
7 y ( − 4 x + 5 )
We see that option 4, 7 y ( − 4 x + 5 ) , matches our factored expression.
Final Answer Therefore, the expression equivalent to − 28 x y + 35 y is 7 y ( − 4 x + 5 ) .
Examples
Factoring expressions is a fundamental skill in algebra and is used in many real-world applications. For example, if you are designing a rectangular garden with an area that can be expressed as − 28 x y + 35 y , where x and y are variables representing dimensions, factoring the expression into 7 y ( − 4 x + 5 ) can help you understand the possible dimensions of the garden in terms of 7 y and ( − 4 x + 5 ) . This can simplify the design process and help you optimize the use of space.
