Question

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Explanation:

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Part (a)

Step1: Simplify the original expression

Combine like terms:
$10x - 6x + 5x = (10-6+5)x = 9x$

Step2: Evaluate each option

• $4x+5x = 9x$ (matches)
• $9+x$ (does not match $9x$)
• $5x-4x = x$ (does not match)
• $9x$ (matches)

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Part (b)

Step1: Expand the original expression

Use the distributive property $a(b+c)=ab+ac$:
$2(1+4y) = 2\cdot1 + 2\cdot4y = 2+8y$

Step2: Evaluate each option

• $2+4y$ (does not match)
• $2\cdot1+2\cdot4y = 2+8y$ (matches)
• $2+8y$ (matches)
• $2+1+2+4y=5+4y$ (does not match)

Answer:

(a) $4x+5x$, $9x$
(b) $2\cdot1+2\cdot4y$, $2+8y$