Question

Factorie (i) (a³-343³)​

Answer 1

$\huge{\mathcal{\underline{\pink{Solution:-}}}}$

(a³ - 343) = (a³ - 7³)

$\large\rm\bold{\underline{\boxed{(a^3-b^3)\:=\:(a-b)(a^2+ab+b^2)}}}$

⇒ (a³ - 7³) = (a - 7)(a² - 7a + 49)

∴ (a³- 343) = (a - 7)( a² - 7a + 49)

$\huge\tt{\underline{\underline{\green{Additional\:information:-}}}}$

❃ (a³+b³) = (a + b)(a² - ab + b²)

❃ (a+b)³ = a³ + b³ + 3ab(a + b)

❃ (a-b)³ = a³ - b³ - 3ab(a - b)

❃ a³ + b³ + c³ = 3abc { only when a+b+c is equal to zero }

Answer 2

$({a}^{ 3} - 343 ^{3} )$

$(a \times a \times a - 7 \times 7 \times 7)$

$value \: of \: a \: = a \: \: and \: b = 7$

$({a}^{3} - {b}^{3} ) = (a - b)( {a}^{2} + ab + {b}^{2} )$

$putting \: the \: value \: of \: a \: and \: b \: in \: the \: factors$

$(a - 7)( (a) ^{2} + 7 \times a + (7)^{2} )$

$(a - 7)( {a}^{2} + 7a + 49 )$

$= > ( {a}^{2} + (7 + 7)a + 49)$

${a}^{2} + 7a + 7a + 49 = 0$

$a(a + 7) + 7(a + 7)$

$(a + 7)(a +7 )$

$( {a}^{2} + 49)$

$so \: the \: factors \: are(a - 7)(a + 7)(a + 7)$

or

$(a - 7)( {a}^{2} + 49)$

hope it will help u dear❣❣❣❣