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Question
Find the product 24x2 (1 − 2x) and evaluate its value for x = 3.
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Solution
To find the product, we will use distributive law as follows:
\[24 x^2 \left( 1 - 2x \right)\]
\[ = 24 x^2 \times 1 - 24 x^2 \times 2x\]
\[ = 24 x^2 - 48 x^{1 + 2} \]
\[ = 24 x^2 - 48 x^3\]
Substituting x = 3 in the result, we get:
\[24 x^2 - 48 x^3 \]
\[ = 24 \left( 3 \right)^2 - 48 \left( 3 \right)^3 \]
\[ = 24 \times 9 - 48 \times 27\]
\[ = 216 - 1296\]
\[ = - 1080\]
Thus, the product is \[(24 x^2 - 48 x^3 )\text {P and its value for x = 3 is } ( - 1080)\].
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