第8类RD Sharma解决方案–第8章代数表达式的除法–练习8.2

问题1.将6x ³ y ² z ²除以3x ² yz

解决方案：

We can write 6x³y²z² as 2 * 3 * x * x * x * y * y * z * z

We can write 3x²yz as 3 * x * x * y * z

Now ans = (6x³y²z²)/(3x²yz)

              = (2 * 3 * x * x * x * y * y * z * z)/(3 * x * x * y * z)

              = 2 * x * y * z

So the answer is 2xyz

问题2.用15m ² n ³除以5m ² n ²

解决方案：

We can write 15m²n³ as 5 * 3 * m * m * n * n * n

We can write 5m²n² as 5 * m * m * n * n

Now ans = (15m²n³)/(5m²n²)

              = (3 * 5 * m * m * n * n * n)/(5 * m * m * n * n)

             = 3 * n

So the answer is 3n

问题3.将24a ³ b ³除以-8ab

解决方案：

We can write 24a³b³ as 3 * 8 * a * a * a * b * b * b

Now ans = (24a³b³)/(-8ab)

              = -(3 * 8 * a * a * a * b * b * b)/(8 * a * b)

              = -(3 * a * a * b * b)

              = -3 * a * a * b * b

We can write -3 * a * a * b * b as -3 * a² * b²

So  the answer is -3a²b²

问题4.用-21abc^{除以-21abc 2}

解决方案：

We can write -21abc² as -3 * 7 * a * b * c * c

We can write 7abc as 7 * a * b * c

Now ans = (-21abc²)/(7abc)

             = -(7 * 3 * a * b * c * c)/(7 * a * b * c)

             = -(3 * c)

             = -3c

So the answer is -3c

问题5.用72xyz ²除以-9xz

解决方案：

We can write 72xyz² as 8 * 9 * x * y * z * z

Now ans = (72xyz²)/(-9xz)

              = -(8 * 9 * x * y * z * z)/(9 * x * z)

              = -(8 * y * z)

              = -8yz

So the answer is -8yz

问题6.用-72a ⁴ b ⁵ c ⁸除以-9a ² b ² c ³

解决方案：

We can write -72a⁴b⁵c⁸ as -8*9*a*a*a*a*b*b*b*b*b*c*c*c*c*c*c*c*c

We can write -9a²b²c³ as -9*a*a*b*b*c*c*c

Now ans = (-72a⁴b⁵c⁸) /(-9a²b²c³)

              = (8*9*a*a*a*a*b*b*b*b*b*c*c*c*c*c*c*c*c) / (9*a*a*b*b*c*c*c)

              = (8*a*a*b*b*b*c*c*c*c*c)

              = 8*a*a*b*b*b*c*c*c*c*c

We can write 8*a*a*b*b*b*c*c*c*c*c as 8 * a² * b³ * c⁵

So the answer is 8a²b³c⁵

问题7.将16 * m ³ * y ²除以4 * m ² * y

解决方案：

We can write 16m³y² as 4 * 4 * m * m * m * y * y

We can write 4m²y as 4 * m * m * y

Now ans = (16m³y²)/(4m²y)

              = (4 * 4 * m * m * m * y * y)/(4 * m * m * y)

              = (4 * m * y)

              = 4my

So the answer is 4my

问题8.将32 * m ² * n ³ * p ²除以4 * m * n * p

解决方案：

We can write 32m²n³p² as 4 * 8 * m * m * n * n * n * p * p

Now ans = (32m²n³p²) / (4mnp)

              = (4 * 8 * m * m * n * n * n * p * p) / (4 * m * n * p))

              = (8 * m * n * n * p)

We can write 8 * m * n * n * p as 8 * m * n² * p

So the answer is 8mn²p