Let's simplify each of the expressions one by one:
a) \(7(x - y)\): \[ 7(x - y) = 7x - 7y \]
B) \(-23 \cdot (2a - 30 + 1)\): First, simplify the expression inside the parentheses: \[ 2a - 30 + 1 = 2a - 29 \] Now, distribute \(-23\): \[ -23(2a - 29) = -46a + 667 \]
c) \((a - 4b) \cdot 3\): Distributing the \(3\): \[ 3(a - 4b) = 3a - 12b \]
d) \(1.5 \cdot (-3x + 4y - 52)\): Distributing \(1.5\): \[ 1.5(-3x) + 1.5(4y) + 1.5(-52) = -4.5x + 6y - 78 \]
So, the simplified forms for each expression are:
a) \(7x - 7y\)
B) \(-46a + 667\)
c) \(3a - 12b\)
d) \(-4.5x + 6y - 78\)
