Simplify the expression. a - 4ab + a2 - 4b / 4b2 - a2b - ab - 4ab2

$$a - 4ab + a^2 - 4b$$

Panga upya vigezo:

$$a^2 + a - 4ab - 4b$$

Weka vigezo pamoja na toa vigezo vya kawaida:

$$a(a+1) - 4b(a+1)$$

Toa $(a+1)$ kama kigezo cha kawaida:

$$(a+1)(a-4b)$$

$$4b^2 - a^2b - ab - 4ab^2$$

Toa $b$ kama kigezo cha kawaida kutoka kwa vigezo vyote:

$$b(4b - a^2 - a - 4ab)$$

Panga upya vigezo ndani ya mabano:

$$b(-a^2 - a + 4b - 4ab)$$

Weka vigezo pamoja ndani ya mabano:

$$b[-a(a+1) + 4b(1-a)]$$

Kwa kuwa hakuna kigezo cha kawaida kati ya nambari $(a+1)(a-4b)$ na kinyume $b[-a(a+1) + 4b(1-a)]$, usemi hauwezi kurahisishwa zaidi kwa kufuta vigezo.
Usemi uliorahisishwa ni:

$$\boxed{\frac{(a+1)(a-4b)}{b[-a(a+1) + 4b(1-a)]}}$$

6. Kutokana na $a = -2$, $b = 5$ na $c = -1$, tathmini.

$$\frac{4a^3 + 5b - c}{\frac{1}{3}(c^2 - a^2)}$$

$$4a^3 + 5b - c = 4(-2)^3 + 5(5) - (-1)$$ $$= 4(-8) + 25 + 1$$ $$= -32 + 25 + 1$$ $$= -7 + 1$$ $$= -6$$

$$\frac{1}{3}(c^2 - a^2) = \frac{1}{3}((-1)^2 - (-2)^2)$$ $$= \frac{1}{3}(1 - 4)$$ $$= \frac{1}{3}(-3)$$ $$= -1$$

$$\frac{-6}{-1} = 6$$

Thamani ya usemi ni $\boxed{6}$.