Question

(a) select all equivalent expressions from the list for the expression.
12x - 6x + 5x
□ 6x + 5x □ 6x - 5x □ 11 + x □ 11x
(b) select all equivalent expressions from the list for the expression.
9(1 + 9y)
□ 9 + 9y □ 9·1 + 9·9y □ 9 + 81y □ 9 + 1·9 + 9y

Explanation:

Step1: Simplify the first expression

Combine like terms: $12x - 6x + 5x = (12-6)x + 5x = 6x + 5x = 11x$

Step2: Match with options (a)

Identify expressions equal to $11x$: $6x+5x$ simplifies to $11x$, and $11x$ is the fully simplified form.

Step3: Expand the second expression

Apply distributive property: $9(1+9y) = 9\cdot1 + 9\cdot9y$

Step4: Simplify the expanded form

Calculate products: $9\cdot1 + 9\cdot9y = 9 + 81y$

Step5: Match with options (b)

Identify expressions equal to $9+81y$: $9\cdot1 + 9\cdot9y$ is the expanded form, and $9+81y$ is the simplified expanded form.

Answer:

(a) 6x+5x, 11x
(b) $9\cdot1 + 9\cdot9y$, $9+81y$