Question

Which statement about the simplified binomial expansion of (a – b)n, where n is a positive integer, is true? All terms of the expansion are positive. All terms in the expansion are negative. The first term in the expansion is positive. The first term in the expansion is negative.

Answer 1

Hi,

✳️ Answer: Option 3 is correct
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The first term in the expansion is positive.


✳️ Explanation:
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Binomial expansion is represented as,if n= 0,1,2,3,...

${(a - b)}^{0} = 1 \\ \\ {(a - b)}^{1} = a - b \\ \\ ( {a - b)}^{2} = {a}^{2} - 2ab + {b}^{2} \\ \\ {(a - b)}^{3} = {a}^{3} - 3 {a}^{2} b + 3a {b}^{2} - {b}^{3} \\ \\ ...$

✔️Thus we can see that first term is positive always.

✔️All the terms are not positive.


✔️All the terms in expansion are not negative


✔️First term is not negative,


✔️✔️Although first term is positive then + and - sign alternatively appears.

So, we can conclude that The first term in the expansion is positive.

Option 3 is correct.

Hope it helps you.