Question

real numbers
identifying equivalent algebraic expressions
for each expression, select all equivalent expressions from the list.
(a) 8(6x - 5) 48x - 5 48x - 40 14x - 5 8·6x - 8·5
(b) 8y + 6y + 3y 17y 9y - 8y 8y + 9y 17 + y

Explanation:

Part (a)

Step1: Apply Distributive Property

The distributive property states that \( a(b - c)=a\cdot b - a\cdot c \). For \( 8(6x - 5) \), we distribute 8 to both terms inside the parentheses:
\( 8(6x - 5)=8\cdot6x-8\cdot5 \)

Step2: Simplify the Products

Calculate \( 8\cdot6x = 48x \) and \( 8\cdot5=40 \), so \( 8(6x - 5)=48x - 40 \) and also \( 8(6x - 5)=8\cdot6x-8\cdot5 \)

Part (b)

Step1: Combine Like Terms

For \( 8y + 6y+3y \), add the coefficients of \( y \). The coefficients are 8, 6, and 3. So \( 8 + 6+3=17 \), thus \( 8y + 6y + 3y=17y \). Also, \( 6y + 3y = 9y \), so \( 8y+6y + 3y=8y + 9y \) (since \( 6y+3y = 9y \))

Answer:

(a) Equivalent expressions: \( 48x - 40 \), \( 8\cdot6x - 8\cdot5 \)
(b) Equivalent expressions: \( 17y \), \( 8y + 9y \)