Question

Please solve this question​

Answer 1

ANSWER:

• Value of the expression:
• $\dfrac{1}{a} (x + a)(ax + 1)$

GIVEN:

$x {}^{2} + \dfrac{a {}^{2} + 1 }{a} x + 1$

TO FIND:

• Factorisation of above expression.

SOLUTION:

$= x {}^{2} + \dfrac{a {}^{2} + 1 }{a} x + 1 \\ \\ = \frac{ax {}^{2} + (a {}^{2} + 1)x + a }{a} \\ \\ = \frac{ax {}^{2} + a {}^{2}x + x + a }{a} \\ \\ = \frac{(ax {}^{2} + a {}^{2} x) + (x +a) }{a} \\ \\ = \frac{ax(x + a) + 1(x + a)}{a} \\ \\ = \frac{(x + a)(ax + 1)}{a} \\ \\ = \frac{1}{a} (x + a)(ax + 1)$

The value of above expression:

$\dfrac{1}{a} (x + a)(ax + 1)$

NOTE:

some important formulas:

• (a+b)² = a²+b²+2ab
• (a-b)² = a²+b²-2ab
• (a+b)³ = a³+b³+3ab(a+b)
• (a+b)³ = a³-b³-3ab(a-b)