Question

(a) select all equivalent expressions from the list for the expression. 8(8x - 5) □ 64x - 5 □ 8·8x - 8·5 □ 16x - 5 □ 64x - 40 (b) select all equivalent expressions from the list for the expression. 12y + 2y + 5y □ 19y □ 12y - 7y □ 12y + 7y □ 19 + y

Explanation:

Step1: Apply distributive property

For \(8(8x - 5)\), use \(a(b-c)=ab-ac\):
\(8 \cdot 8x - 8 \cdot 5\)

Step2: Calculate the products

Compute each term:
\(64x - 40\)

Step3: Combine like terms (part b)

For \(12y + 2y + 5y\), first group \(2y+5y\):
\(12y + (2y + 5y) = 12y + 7y\)

Step4: Simplify the sum (part b)

Add the coefficients:
\(19y\)

Answer:

(a) \(8 \cdot 8x - 8 \cdot 5\), \(64x - 40\)
(b) \(12y + 7y\), \(19y\)