第8类RD Sharma解决方案–第8章代数表达式的除法–练习8.6

问题1：将x ² – 5x + 6除以(x – 3)

解决方案：

(x2 – 5x + 6)/(x-3)

Factorise the numerator and then divide it by (x-3):

x² – 5x + 6

= x² – 3x – 2x + 6

= (x² – 3x – 2x + 6)/(x – 3)

= (x(x – 3) – 2(x – 3))/(x – 3)

= ((x – 3)(x – 2))/(x – 3)

= (x – 2)

Therefore, the answer is (x-2).

问题2：除以斧头² – AY ²由(AX + AY)

解决方案：

(ax² – ay²)/(ax + ay)

= a(x² – y²)/(ax + ay)

= a(x – y)(x + y)/a(x + y)

= x – y

Therefore, the answer is (x – y).

问题3：将(x ⁴ – y ⁴⁾除以(x ² – y ² )

解决方案：

(x⁴ – y⁴)/(x² – y²)

= ((x²)² – (y²)²)/(x² – y²)

= ((x² – y²) (x² + y²)) / (x² – y²)

= x² + y²

Therefore, the answer is (x² + y²).

问题4：将(acx ² +(bc + ad)x + bd)除以(ax + b)

解决方案：

(acx² + (bc + ad)x + bd) / (ax + b)

= (acx² + bcx + adx + bd) / (ax + b)

= (cx(ax + b) + d(ax + b)) / (ax + b)

= (ax + b)(cx + d) / (ax + b)

= cx + d

Therefore, the answer is (cx + d).

问题5：将(a ² + 2ab + b ² )–(a ² + 2ac + c ² )除以(2a + b + c)

解决方案：

((a² + 2ab + b²) – (a² + 2ac + c²)) / (2a + b + c)

= ((a + b)² – (a + c)²) / (2a + b + c)

= ((a + b + a + c)(a + b – a – c)) / (2a + b + c)

= (2a + b + c)(b – c) / (2a + b + c)

= b – c

Therefore, the answer is (b – c).

问题6：将((1/4)x ² –(1/2)x – 12)除以((1/2)x – 4)

解决方案：

(1/4)x² – (1/2)x – 12

= (1/4)(x² – 2x – 48)

Now factorize it:

= (1/4)(x² – 8x + 6x – 48)

= (1/4)(x(x – 8) + 6(x – 8))

= (1/4)(x – 8)(x + 6)

Now divide it by (1/2)x – 4:

= (1/4)(x – 8)(x + 6) / ((1/2)x – 4)

= (1/4)(x – 8)(x + 6) / (1/2)(x – 8)

= (1/4)(2/1)(x + 6)

= (1/2)x + 3

Therefore, the answer is (1/2)x + 3.