Question

5 (x + 7y) - 4 (y - 7x)?

Explanation:

Step1: Distribute the coefficients

First, we distribute the 5 and -4 into the parentheses.
For \(5(x + 7y)\), we get \(5x + 35y\) (using the distributive property \(a(b + c)=ab + ac\) where \(a = 5\), \(b = x\), and \(c = 7y\)).
For \(-4(y - 7x)\), we get \(-4y + 28x\) (using the distributive property \(a(b - c)=ab - ac\) where \(a=-4\), \(b = y\), and \(c = 7x\)).
So the expression becomes \(5x + 35y-4y + 28x\).

Step2: Combine like terms

Now we combine the like terms (terms with \(x\) and terms with \(y\)).
For the \(x\) terms: \(5x + 28x=(5 + 28)x = 33x\) (using the commutative property of addition and the distributive property in reverse).
For the \(y\) terms: \(35y-4y=(35 - 4)y = 31y\) (using the commutative property of addition and the distributive property in reverse).

Putting these together, the simplified expression is \(33x + 31y\).

Answer:

\(33x + 31y\)