Question

Expond the following (5x-4)^3
$expond \: the \: following \\ (5x - 4)^2$
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Answer 1

$( {5x - 4})^{3} \\ = ({5x})^{3} - ( {4})^{3} \\ =( {125x}^{3} ) - (64) \\ {125x}^{3} - 64$

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Answer 2

Step-by-step explanation:

${(5x - 4)}^{3} \\ {(5x)}^{3} - {4}^{3} - 3 \times {(5x)}^{2} \times 4 + 3 \times 5x \times {4}^{2} \\ 125 {x}^{3} - 64 - 3 \times 25 {x}^{2} \times 4 + 3 \times 5x \times 16 \\ 125 {x}^{3} - 64 - 300 {x}^{2} + 240 x \\ 125 {x}^{3} - 300 {x}^{2} + 240x - 64$

${(5x - 4)}^{2} \\ {(5x)}^{2} - 2 \times 5x \times 4 + {4}^{2} \\ 25 {x}^{2} - 40x + 16$

• first one is done by the identity :

(a - b)^3 = a^3 - b^3 - 3a^2b + 3ab^2

• second one is done by the identity:

(a - b)^2 = a^2 - 2ab + b^2