Question

A) (-6а2 + 4): (2а); б)(-7х3 + 14х2 – 21х): (-7х); в) (9а3с – 6а2с2): 3а2с2;

Answer 1

$a) \frac{ - 6a {}^{2} + 4}{2a} = \frac{ 2( - 3a + 2)}{2a} = \frac{ - 3a + 2}{a}$

$b)\frac{- 7{x}^{3} + 14 {x}^{2} - 21x}{ - 7x} = \frac{ - 7x( {x}^{2} - 2x + 3) }{ - 7x} = x {}^{2} - 2x + 3$

в)

$\frac{ {9a}^{3} c -6 {a}^{2} {c}^{2} }{3 {a}^{2} {c}^{2} } = \frac{3 {a}^{2} {c}^{} (3 a - 2c)}{3a {}^{2} c {}^{2} } = \frac{3a - 2c}{c}$

Answer 2

Let's solve the given expressions step by step:

a) (-6a^2 + 4) / (2a)

To simplify this expression, we can divide each term by 2a:

(-6a^2 + 4) / (2a) = -6a^2 / (2a) + 4 / (2a) = -3a + 2/a

Therefore, the simplified expression is -3a + 2/a.

b) (-7x^3 + 14x^2 – 21x) / (-7x)

Dividing each term by -7x, we get:

(-7x^3 + 14x^2 – 21x) / (-7x) = (-7x^3 / (-7x)) + (14x^2 / (-7x)) – (21x / (-7x)) = x^2 - 2x + 3

So, the simplified expression is x^2 - 2x + 3.

c) (9a^3c – 6a^2c^2) / (3a^2c^2)

Dividing each term by 3a^2c^2, we have:

(9a^3c – 6a^2c^2) / (3a^2c^2) = (9a^3c / (3a^2c^2)) - (6a^2c^2 / (3a^2c^2)) = 3ac - 2c

Therefore, the simplified expression is 3ac - 2c.

I hope this helps! Let me know if you have any further questions.