Question

Evaluate each expression using the distributive property. a. \(17 \cdot(52-2)\) b. \((90-7) \cdot 5\)

Short answer

Question: Use the distributive property to evaluate and simplify the following expressions: a) \(17\cdot(52-2)\) b) \((90-7) \cdot 5\) Please provide your answers.

Step-by-step solution

Part a: \(17 \cdot(52-2)\)

Apply the distributive property: \(17 \cdot(52-2) = 17 \cdot 52 - 17 \cdot 2\). Now, perform the required multiplications: \(17 \cdot 52 - 17 \cdot 2 = 884 - 34\). Finally, subtract: \(884 - 34 = 850\). So, \(17\cdot(52-2)=850\).

Part b: \((90-7) \cdot 5\)

Apply the distributive property: \((90-7) \cdot 5 = 90 \cdot 5 - 7 \cdot 5\). Now, perform the required multiplications: \(90 \cdot 5 - 7 \cdot 5 = 450 - 35\). Finally, subtract: \(450 - 35 = 415\). So, \((90-7) \cdot 5=415\).