8类RD Sharma解决方案–第六章代数表达式和恒等式–练习6.7

问题1.查找以下产品：

(i)(x + 4)(x + 7)

解决方案：

By simplifying the given expression, we get

x (x + 7) + 4 (x + 7)

x² + 7x + 4x + 28

x²+ 11x + 28

(ii)(x – 11)(x + 4)

解决方案：

By simplifying the given expression, we get

x (x + 4) – 11 (x + 4)

x² + 4x – 11x – 44

x² – 7x – 44

(iii)(x + 7)(x – 5)

解决方案：

By simplifying the given expression, we get

x (x – 5) + 7 (x – 5)

x² – 5x + 7x – 35

x² + 2x – 35

(iv)(x – 3)(x – 2)

解决方案：

By simplifying the given expression, we get

x (x – 2) – 3 (x – 2)

x² – 2x – 3x + 6

x² – 5x + 6

(v)(y ² – 4)(y ² – 3)

解决方案：

By simplifying the given expression, we get

y² (y²– 3) – 4 (y² – 3)

y⁴ – 3y² – 4y² + 12

y⁴ – 7y² + 12

(六)(x + 4/3)(x + 3/4)

解决方案：

By simplifying the given expression, we get

x (x + 3/4) + 4/3 (x + 3/4)

x² + 3x/4 + 4x/3 + 12/12

x² + 3x/4 + 4x/3 + 1

x² + 25x/12 + 1

(vii)(3x + 5)(3x + 11)

解决方案：

By simplifying the given expression, we get

3x (3x + 11) + 5 (3x + 11)

9x² + 33x + 15x + 55

9x² + 48x + 55

(viii)(2x ² – 3)(2x ² + 5)

解决方案：

By simplifying the given expression, we get

2x²(2x² + 5) – 3 (2x² + 5)

4x⁴ + 10x² – 6x² – 15

4x⁴ + 4x² – 15

(ix)(z ² + 2)(z ² – 3)

解决方案：

By simplifying the given expression, we get

z² (z² – 3) + 2 (z² – 3)

z⁴ – 3z² + 2z² – 6

z⁴– z² – 6

(x)(3x – 4y)(2x – 4y)

解决方案：

By simplifying the given expression, we get

3x (2x – 4y) – 4y (2x – 4y)

6x² – 12xy – 8xy + 16y²

6x² – 20xy + 16y²

(xi)(3x ² – 4xy)(3x ² – 3xy)

解决方案：

By simplifying the given expression, we get

3x² (3x² – 3xy) – 4xy (3x² – 3xy)

9x⁴ – 9x³y – 12x³y + 12x²y²

9x⁴ – 21x³y + 12x²y²

(xii)(x + 1/5)(x + 5)

解决方案：

By simplifying the given expression, we get

x (x + 1/5) + 5 (x + 1/5)

x² + x/5 + 5x + 1

x² + 26/5x + 1

(xiii)(z + 3/4)(z + 4/3)

解决方案：

By simplifying the given expression, we get

z (z + 4/3) + 3/4 (z + 4/3)

z² + 4/3z + 3/4z + 12/12

z²+ 4/3z + 3/4z + 1

z² + 25/12z + 1

(xiv)(x ² + 4)(x ² + 9)

解决方案：

By simplifying the given expression, we get

x² (x² + 9) + 4 (x²+ 9)

x⁴ + 9x² + 4x² + 36

x⁴ + 13x²+ 36

(xv)(y ² + 12)(y ² + 6)

解决方案：

By simplifying the given expression, we get

y² (y²+ 6) + 12 (y² + 6)

y⁴+ 6y² + 12y² + 72

y⁴ + 18y² + 72

(xvi)(y ² + 5/7)(y ² – 14/5)

解决方案：

By simplifying the given expression, we get

y² (y² – 14/5) + 5/7 (y² – 14/5)

y⁴ – 14/5y² + 5/7y² – 2

y⁴ – 73/35y² – 2

(xvii)(p ² + 16)(p ² – 1/4)

解决方案：

By simplifying the given expression, we get

p² (p² – 1/4) + 16 (p² – 1/4)

p⁴ – 1/4p² + 16p² – 4

p⁴ + 63/4p² – 4

问题2：评估以下内容：

(i)102×106

解决方案：

By simplifying the given expression, we get

102 × 106 = (100 + 2) (100 + 6)

= 100 (100 + 6) + 2 (100 + 6)

= 10000 + 600 + 200 + 12

= 10812

(ii)109×107

解决方案：

By simplifying the given expression, we get

109 × 107 = (100 + 9) (100 + 7)

= 100 (100 + 7) + 9 (100 + 7)

= 10000 + 700 + 900 + 63

= 11663

(iii)35×37

解决方案：

By simplifying the given expression, we get

35 × 37 = (30 + 5) (30 + 7)

= 30 (30 + 7) + 5 (30 + 7)

= 900 + 210 + 150 + 35

= 1295

(iv)53×55

解决方案：

By simplifying the given expression, we get

53 × 55 = (50 + 3) (50 + 5)

= 50 (50 + 5) + 3 (50 + 5)

= 2500 + 250 + 150 + 15

= 2915

(v)103×96

解决方案：

By simplifying the given expression, we get

103 × 96 = (100 + 3) (100 – 4)

= 100 (100 – 4) + 3 (100 – 4)

= 10000 – 400 + 300 – 12

= 10000 – 112

= 9888

(vi)34×36

解决方案：

By simplifying the given expression, we get

34 × 36 = (30 + 4) (30 + 6)

= 30 (30 + 6) + 4 (30 + 6)

= 900 + 180 + 120 + 24

= 1224

(vii)994×1006

解决方案：

By simplifying the given expression, we get

994 × 1006 = (1000 – 6) (1000 + 6)

= 1000 (1000 + 6) – 6 (1000 + 6)

= 1000000 + 6000 – 6000 – 36

= 999964