8级RD Sharma解决方案–第7章分解–练习7.1

问题1.查找(GCF / HCF)为2x ²和12x ²

解决方案：

First Prime Factorize each monomial, then find common among them.

Here,

2x² = 2 * x * x

12x² = 2* 2 * 3 * x * x

GCF(2x², 12x²) = 2 * x * x

                          = 2x²

问题2.查找(GCF / HCF)为6x ³ y和18x ² y ³

解决方案：

First Prime Factorize each monomial, then find common among them.

Here,

6x³y = 2 * 3 * x * x * x * y

18x²y³ = 2 * 2 * 3 * x * x * y * y * y

GCF(6x³y, 18x²y³) = 2 * 3 * x * x * y

                               = 6x²y

问题3.查找(GCF / HCF)为7x，21x ²和14xy ²

解决方案：

First Prime Factorize each monomial, then find common among them.

Here,

7x = 7 * x

21x² = 7 * 3 * x * x

14xy² = 7 * 2 * x * y * y

GCF(7x, 21x², 14xy²) = 7*x

                                    = 7x

问题4.查找(GCF / HCF)为42x ² yz和63x ³ y ² z ³

解决方案：

First Prime Factorize each monomial, then find common among them.

Here,

42x²yz = 2 * 3 * 7 * x * x * y * z

63x³y²z³ = 3 * 3 * 7 * x * x * x * y * y * z * z * z

GCF(42x²yz, 63x³y²z³) = 3 * 7 * x * x * y * z

                                       = 21x²yz

问题5.查找的12ax ^2(GCF / ^{HCF)，6α2×3}和2a ^3×5

解决方案：

First Prime Factorize each monomial, then find common among them.

Here,

12ax² = 2 * 2 * 3 * a * x * x

6a²x³ = 2 * 3 * a * a * x * x * x

2a³x⁵ = 2 * a * a * a * x * x * x * x * x

GCF(12ax², 6a²x³,2a³x⁵) = 2 * a * x * x

                                         = 2ax²

问题6.查找的9X ^2(GCF / HCF)，15X ² Y ^{3，6xy 2}和21X ² Y ²

解决方案：

First Prime Factorize each monomial, then find common among them.

Here,

9x² = 3 * 3 * x * x

15x²y³ = 3 * 5 * x * x * y * y * y

6xy² = 2 * 3 * x * y * y

21x²y² = 3 * 7 * x * x * y * y

GCF(9x², 15x2y³, 6xy² and 21x²y²) = 3 * x

                                                           = 3x

问题7.查找(GCF / HCF)为4a ² b ³ ，-12a ³ b，18a ⁴ b ³

解决方案：

First Prime Factorize each monomial, then find common among them.

Here,

4a²b³ = 2 * 2 * a * a * b * b * b

-12a³b = -1 * 2 * a * a * a * b

18a⁴b³ = 2 * 3 * 3 * a * a * a * a * b * b * b

GCF(4a²b³, -12a³b, 18a⁴b³) = 2 * a * a * b

                                              = 2a²b                                                    

问题8.查找^6×2 Y ²的(GCF / HCF)，9XY ^3，3×3的Y ²

解决方案：

First Prime Factorize each monomial, then find common among them.

Here,

6x²y² = 2 * 3 * x * x * y * y

9xy³ = 3 * x * y * y * y

3x³y² = 3 * x * x * x * y * y

GCF(6x²y², 9xy³, 3x³y²) = 3 * x * y * y

                                        = 3xy²                                           

^{问题9.查找(2)} b ³ ，a ³ b ^2的(GCF / HCF)

解决方案：

First Prime Factorize each monomial, then find common among them.

Here,

a²b³ = a * a * b * b * b

a³b² = a * a * a * b * b

GCF(a²b³, a³b²) = a * a * b * b

                           = a²b²

问题10查找36A ² B ² C ⁴的(GCF / HCF)，54A ⁵ C ^{2，90A 4b的2} C ²

解决方案：

First Prime Factorize each monomial, then find common among them.

Here,

36a²b²c⁴ = 2 * 2 * 3 * 3 * a * a * b * b * c * c * c * c

54a⁵c² = 2 * 3 * 3 * 3 * a * a * a * a * a * c * c

90a⁴b²c² = 2 * 3 * 3 * 5 * a * a * a * a * b * b * c * c

GCF(36a²b²c⁴, 54a⁵c², 90a⁴b²c²) = 2 * 3 * 3 * a * a * c * c

                                                      = 18a²c²

问题11.找到(GCF / HCF)x ³ ，-yx ²

解决方案：

First Prime Factorize each monomial, then find common among them.

Here,

x³ = x * x * x

-yx² = -1 * y * x * x

GCF(x³, -yx²) = x * x

                       = x²

问题12.发现(GCF / HCF)为15a ³ ，-45a ² ，-150a

解决方案：

First Prime Factorize each monomial, then find common among them.

Here,

15a³ = 3 * 5 * a * a * a

-45a² = -1 * 3 * 3 * 5 * a *a

-150a = -1 * 2 * 3 * 5 * 5 * a

GCF(15a³, -45a², -150a) = 3 * 5 * a

                                        = 15a

问题13查找的^2×3的Y ^2(GCF / HCF)，10X ² Y ^3，14xy

解决方案：

First Prime Factorize each monomial, then find common among them.

Here,

2x³y² = 2 * x * x * x * y * y

10x²y³ = 2 * 5 * x * x * y * y * y

14xy = 2 * 7 * x * y

GCF(2x³y², 10x²y³, 14xy) = 2 * x * y

                                           = 2xy

问题14查找的14倍³ Y ^5(GCF / HCF)，10倍的⁵ Y ^3，2×2 Y ²

解决方案：

First Prime Factorize each monomial, then find common among them.

Here,

14x³y⁵ = 2 * 7 * x * x * x * y * y * y * y * y

10x⁵y³ = 2 * 5 * x * x * x * x * x * y * y * y

2x²y² = 2 * x * x * y * y

GCF(14x³y⁵, 10x⁵y³, 2x²y²) = 2 * x * x * y * y

                                              = 2x²y²

在以下表达式中找到这些术语的最大公因子(GCF)。 (Q15-Q17)

问题15. 5a ⁴ + 10a ³ – 15a ²

解决方案：

Here, 5a⁴ = 5 * a * a * a * a

         10a³ = 2 * 5 * a * a * a

         -15a² = -1 * 3 * 5 * a * a

5a⁴ + 10a³ – 15a² = (5 * a * a * a * a) + (2 * 5 * a * a * a) + (-1 * 3 * 5 * a * a)

                            = 5a²(a² + 2a – 3)

GCF(5a⁴ + 10a³ – 15a²) = 5a²

问题16. 2xyz + 3x ² y + 4y ²

解决方案：

Here, 2xyz = 2 * x * y * z

          3x²y = 3 * x * x * y

           4y² = 2 * 2 * y * y

2xyz + 3x²y + 4y² = (2 * x * y * z) + (3 * x * x * y) + (4 * y * y)

                             = y(2x + 3x² + 4y)

GCF(2xyz + 3x²y + 4y²) = y

问题17.3a ² b ² + 4b ² c ² + 12a ² b ² c ²

解决方案：

Here, 3a²b² = 3 * a * a * b * b

          4b²c² = 2 * 2 * b * b * c * c

          12a²b²c² = 2 * 2 * 3 * a * a * b * b * c * c

3a²b² + 4b²c² + 12a²b²c² = (3 * a * a * b * b) + (2 * 2 * b * b * c * c) + (2 * 2 * 3 * a * a * b * b * c * c)

                                         = b(3a²b + 4bc² + 12a²bc²)

GCF(3a²b² + 4b²c² + 12a²b²c²) = b