Question

125a⁸b⁴-20a⁶b⁵ ______________ 15a⁵b⁴

Answer 1

$\displaystyle\bf\\\frac{125a^{8} b^{4}-20a^{6} b^{5} }{15a^{5} b^{4} } =\frac{5a^{5} b^{4} \cdot(25a^{3} -2ab)}{3\cdot 5a^{5} b^{4} } =\frac{25a^{3}-2ab }{3}$

Answer 2

To simplify the expression:

(125a⁸b⁴ - 20a⁶b⁵) / (15a⁵b⁴)

First, let's factor out the common terms from the numerator:

125a⁸b⁴ = 5³ * a⁸ * b⁴ = (5a²)³ * (b²)²

20a⁶b⁵ = 2² * 5 * a⁶ * b⁵ = (2a²)² * 5 * a² * b⁴

Now, substitute the factored terms back into the expression:

(5a²)³ * (b²)² - (2a²)² * 5 * a² * b⁴

To simplify further, let's divide the common factors:

(5a²)³ * (b²)² / (15a⁵b⁴)

The common factors cancel out, leaving us with:

(5a²)³ * (b²)² / (3a⁵)

This can be simplified as:

5³ * a²³ * b²² / 3a⁵

Rearranging the terms:

125a²³ * b²² / 3a⁵

Simplifying the exponents:

125a^(2+3) * b^(2+2) / 3a⁵

125a⁵ * b⁴ / 3a⁵

Now, divide the common terms:

125/3 * a⁵/a⁵ * b⁴

The a⁵ terms cancel out:

125/3 * b⁴

Therefore, the simplified expression is:

125/3 * b⁴