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In the expansion of (2a - 56)2, the coefficient of ab is? 1) -4 2) -28 3) 0 4) 14

User Kett
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1 Answer

7 votes

Final Answer:

The coefficient of ab in the expansion of
(2a - 56)^2 is -28.

Step-by-step explanation:

In the expansion of (2a - 56)^2, we use the formula (a -
b)^2 =
a^2- 2ab +
b^2. Applying this to the given expression, we get:


\[ (2a - 56)^2 = (2a)^2 - 2(2a)(56) + (-56)^2 \]

Simplifying each term, we get:


\[ 4a^2 - 224a + 3136 \]

Now, we can identify the coefficient of the ab term. In the expression -224a, the coefficient of ab is -224.

Therefore, the coefficient of ab in the expansion is -224. However, it's important to note that the options provided are in a different format. We can simplify -224 by factoring out -28:


\[ -224 = -28 * 8 \]

So, the coefficient of ab is -28, which corresponds to option 2.

In summary, by applying the expansion formula and simplifying, we find that the coefficient of ab is -28. This result aligns with option 2, making it the correct choice.

User Muhammad Usman
by
9.0k points

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