Question

1. 16(m - 2n) and 16m - 32n
2. 15m + 45n + 13 and 5(3m + 9n +

Explanation:

Step1: Expand the first - expression in (4)

Use the distributive property \(a(b - c)=ab - ac\). For \(16(m - 2n)\), we have \(16\times m-16\times2n = 16m-32n\).

Step2: Compare the two expressions in (4)

Since \(16(m - 2n)=16m - 32n\), the two expressions \(16(m - 2n)\) and \(16m - 32n\) are equivalent.

Step3: Expand the second - expression in (6)

For \(5(3m + 9n+?)\) (assuming the full expression is \(5(3m + 9n + k)\)). Using the distributive property \(a(b + c + d)=ab+ac + ad\), we get \(5\times3m+5\times9n+5k=15m + 45n+5k\).
If the second expression is \(5(3m + 9n + 13/5)\), then \(5(3m + 9n+\frac{13}{5})=15m + 45n+13\). But if it is \(5(3m + 9n + k)\) where \(k
eq\frac{13}{5}\), the two expressions are not equivalent. Without the full - term in the second parenthesis of (6), we can't fully conclude. But if we assume the second expression in (6) is \(5(3m + 9n+\frac{13}{5})\):

Answer:

The expressions in (4) are equivalent. The equivalence of the expressions in (6) depends on the full - term inside the second parenthesis. If the second expression in (6) is \(5(3m + 9n+\frac{13}{5})\), they are equivalent; otherwise, they are not.