Class maths students are Interesting.all the best guy for you homework

1. Multiply:
Question 1.
(5x + 3) by (7x + 2)
Solution:
(5x + 3) x (7x + 2)
= 5x (7x + 2) + 3 (7x + 2)
= 35x2
+ 10x + 21x + 6
= 35x2
+ 31x + 6
Question 2.
(2x + 8) by (x – 3)
Solution:
(2x + 8) x (x – 3)
= 2x (x – 3) + 8 (x – 3)
= 2x2
– 6x + 8x – 24
= 2x2
+ 2x – 24
Question 3.
(7x +y) by (x + 5y)
Solution:
(7x + y) x (x + 5y)
= 7x (x + 5y) + y (x + 5y)
= 7x2
+ 35xy + xy + 5y2
=7x2
+ 36xy + 5y2
Question 4.
(a – 1) by (0.1a2
+ 3)
Solution:
(a – 1) x (0.1a2
+ 3)
= a (0.1a2
+ 3) – 1 (0.1a2
+ 3)
= 0.1a3
+ 3a-0.1a2
-3
= 0.1a3
– 0.1a2
+ 3a-3
Question 5.
(3x2
+y2
) by (2x2
+ 3y2
)
Solution:
(3x2
+y2
) x (2x2
+ 3y2
)
= 3x2
(2x2
+ 3y2
) + y2
(2x2
+ 3y2
)
= 6x2 +2
+ 9x2
y2
+ 2x2
y2
+ 3y2 + 2
= 6x4
+ 11 x2
y2
+ 3y4
Question 6.

2. Solution:
Question 7.
(x6
-y6
) by (x2
+y2
)
Solution:
(x6
– y6
) x (x2
+ y2
)
= x6
(x2
+ y2
) – y6
(x2
+ y2
)
= x6
x x2
+ x6
y2
– x2
y6
-y6
x y2
= x6 + 2
+ x6
y2
– x2
y6
– y6 +2
= x + x6
y2
– x2
y6
– y8
Question 8.
(x2
+ y2
) by (3a+2b)
Solution:
(x2
+ y2
) x (3a + 2b)
= x2
(3a + 2b) + y2
(3a + 2b)
= 3x2
a + 2x2
b + 3y2
a + 2y2
b
3ax2
+ 3av2
+ 2bx2
+ 2by2
Question 9.
[-3d + (-7ƒ)] by (5d +ƒ)
Solution:
[-3d + (-7ƒ)] x (5d +ƒ)
= -3d x (5d +ƒ) + (-7ƒ) x (5d +ƒ)
= -15d2
-3dƒ- 35dƒ- 7ƒ2
= -15d2
– 38dƒ- 7ƒ2

3. Question 10.
(0.8a – 0.5b) by (1.5a -3b)
Solution:
(0.8a – 0.5b) x (1.5a-3b)
= 0.8a x (1.5a – 36) – 0.56 (1.5a -3b)
= 1.2a2
– 2.4ab – 0.75ab + 1.5b2
= 1.2a2
-3.15ab+ 1.5b2
Question 11.
(2x2
y2
– 5xy2
) by (x2
-y2
)
Solution:
(2x2
y2
– 5xy2
) x (x2
-y2
)
= 2x2
y2
(x2
– y2
) – 5x_y2
(x2
– y2
)
= 2x2
y2
x x2
– 2x2
y2
xy2
– 5xy2
x x2
+ 5x2
xy2
= 2x2 + 2
y2
– 2x2
x y2 + 2
– 5x1+2
y2
+5xy2 + 2
= 2x4
y2
– 2x2
y4
– 5x3
y2
+ 5xy4
Question 12.
Solution:
Question 13.
Solution:

4. Question 14.

5. Solution:
Question 15.
(2x2
-1) by (4x3
+ 5x2
)
Solution:
(2x2
-1)x(4x3
+ 5x2
)
= 2x2
x (4x3
+ 5x2
) – 1 (4x3
+ 5x2
)
= 2x2
x 4x3
+ 2x2
x 5x2
– 4x3
– 5x2
= 8x2 + 3
+ 10x2 + 2
-4x3
-5x2
= 8x5
+ 10x4
– 4x3
– 5x2
Question 16.
(2xy + 3y2
) (3y2
– 2)
Solution:
(2xy + 3y2
) (3y2
– 2)
= 2xy x (3y2
-2) + 3y2
x (3y2
-2)
= 2xy x Zy2
+ 2xy x (-2) + Zy2
x Zy2
– Zy2
x 2
= 6xy1 + 2
– 4xy + 9y2 + 2
– 6y2
= 6xy3
– 4xy + 9y4
– 6y2
Find the following products and verify the result for x = -1, y = -2 :
Question 17.
(3x-5y)(x+y)
Solution:

6. (3x-5y)(x+y)
= 3x x (x + y) – 5y x (x + y)
= 3x x x + 3x x y-5y x x-5y x y
= 3x2
+ 3xy – 5xy – 5y2
= 3x2
– 2xy – 5y2
Verfification:
x = -1,y = -2
L.H.S. = (3x-5y)(x+y)
= [3 (-1) -5 (-2)] [-1 – 2]
= (-3 + 10) (-3) = 7 x (-3) = -21
R.H.S. = 3x2
– 2xy – 5y2
= 3 (-1)2
– 2 (-1) (-2) -5 (-2)2
=3×1-4-5×4=3-4-20
= 3-24 = -21
∴ L.H.S. = R.H.S.
Question 18.
(x2
y-1) (3-2x2
y)
Solution:
(x2
y-1) (3-2x2
y)
= x2
y (3 – 2x2
y) -1(3-2x2
y)
= x2
y x 3 – x2
y x 2x2
y – 1 x 3 + 1 x 2x2
y
= 3x2
y-2x2 + 2
x y1 +1
-3 + 2x2
y
= 3x2
y – 2x4
y2
– 3 + 2x2
y
= 3x2
y + 2x2
y – 2x4
y2
– 3
= 5x2
y – 2x4
y2
– 3
Verification : (x = -1, y = -2)
L.H.S. = (x2
y – 1) (3 – 2x2
y)
= [(-1)2
x (-2) -1] [3 – 2 x (-1)2 x (-2)]
= [1 x (-2) -1) [3 – 2 x 1 x (-2)]
= (-2 – 1) (3 + 4) = -3 x 7 = -21
R.H.S. = 5x2
y – 2x4
y2
– 3
= 5 (-1)2
(-2) -2 (-1)4
(-2)2
-3
5 x 1 (-2) – 2 (1 x 4) -3
= -10-8-3 = -21
∴ L.H.S. = R.H.S
Question 19.
Solution:

8. Simplify :
Question 20.
x2
(x + 2y) (x – 3y)
Solution:
x2
(x + 2y) (x – 3y)
= x2
[x (x – 3y) + 2y (x – 3y)]
= x2
[x2
– 3xy + 2xy – 6y2
]
= x2
[x2
– xy – 6y2
)
= x2
x x2
– x2
x xy – x2
6y2
= x4
– x3
y – 6x2
y2
Question 21.
(x2
– 2y2
) (x + 4y)
Solution:
(x2
– 2y2
) (x + 4y) x2
y2
= [x2
(x + 4y) -2y2
(x + 4y)] x2
y2
= (x3
+ 4x2
y – 2xy2
– 8y3
) x2
y2
= x2
y2
x x3
+ x2
y2
x 4x2
y – 2x2
y2
x xy2
– 8x2
y2
x y3
= x2 +3
y2
+ 4x2 + 2
y2 +1
– 2x2 +1
y2+ 2
– 8x2
y2+3
= xy + 44
xy3
– 2x3
y4
– 8x2
y5
Question 22.
a2
b2
(a + 2b) (3a + b)
Solution:
a2
b2
(a + 2b) (3a + b)
= a2
b2
[a (3a + b).+ 2b (3a + b)]
= a2
b2
[3a2
+ ab + 6ab + 2b2
]
= a2
b2
[3a2
+ lab + 2b2
]

9. = a2
b2
x 3a2
+ a2
b2
x 7ab + a2
b2
x 2b2
= 3a2 + 2
b2
+ 7a2+1
b2+1
+ 2a2
b2 + 2
= 3a4
b2
+ 7a3
b3
+ 2a2
b4
Question 23.
x2
(x-y) y2
(x + 2y)
Solution:
x2
(x -y) y2
(x + 2y)
= [x2
x x – x2
x y] [y2
x x + y2
x 2y]
= (x3
– x2
y) (xy2
+ 2y3
)
= x3
(xy2
+ 2y3
) – x2
y (xy2
+ 2y3
)
= x3
x xy2
+ x3
x 2y3
– x2
y x xy2
– x2
y x 2y3
= x3 +1
y2
+ 2x3
y3
– x2 +1
y1+ 2
– 2x2
y1 + 3
= x4
y2
+ 2x3
y3
– x3
y3
– 2x2
y4
= x4
y2
+ x3
y3
– 2x2
y4
Question 24.
(x3
– 2x2
+ 5x-7) (2x-3)
Solution:
(x3
– 2x2
+ 5x – 7) (2x – 3)
= (2x – 3) (x3
– 2x2
+ 5x – 7)
= 2x (x3
– 2x2
+ 5x – 7) -3 (x3
– 2x2
+ 5x – 7)
= 2x x x3
– 2x x 2x2
+ 2x x 5x – 2x x 7 -3 x x3
– 3 x (-2x2
) – 3 x 5x – 3 x (-7)
= 2x4
-4x3
+ 10x2
– 14x-3x3
+ 6x2
– 15x + 21
= 2x4
– 4x3
– 3x3
+ 10x2
+ 6x2
– 14x- 15x + 21
= 2x4
-7x3
+ 16x2
-29x+ 21
Question 25.
(5x + 3) (x – 1) (3x – 2)
Solution:
(5x + 3) (x – 1) (3x – 2)
= (5x + 3) [x (3x – 2) -1 (3x – 2)]
= (5x + 3) [3x2
– 2x – 3x + 2]
= (5x + 3) [3x2
– 5x + 2]
= 5x (3x2
– 5x + 2) + 3 (3x2
– 5x + 2)
= (5x x 3x2
– 5x x Sx + 5x x 2)+ [3 x 3x2
+ 3 x (-5x) + 3×2]
= 15x3
– 25x2
+ 10x + 9x2
– 15x + 6
= 15x3
– 25x2
+ 9x2
+ 10x – 15x + 6
= 15x3
– 16x2
– 5x + 6
Question 26.
(5-x) (6-5x) (2-x)
Solution:
(5-x) (6-5x) (2-x)
= [5 (6 – 5x) -x (6 – 5x)] (2 – x)
= [30 – 2$x – 6x + 5x2
] (2 – x)
= (30 – 3 1x + 5x2
) (2-x)
= 2 (30 – 31x + 5x2
) – x (30 – 31x + 5x2
)

10. = 60 – 62x + 10x2
– 30x + 3 1x2
– 5x3
= 60 – 62x – 30x + 10x2
+ 3 1x2
– 5x3
= 60 – 92x + 41x2
– 5x3
Question 27.
(2x2
+ 3x – 5) (3x2
– 5x + 4)
Solution:
(2x2
+ 3x – 5) (3x2
– 5x + 4)
= 2x2
(3x2
– 5x + 4) + 3x (3x2
– 5x + 4) -5 (3x2
– 5x + 4)
= 2x2
x 3x2
– 2x2
x 5x + 2x2
x 4 + 3x x 3x2
– 3x x 5x + 3x x 4 – 5 x 3x2
– 5 (-5x) -5×4
= 6x4
– 10x3
+ 8x2
+ 9x3
– 15x2
+ 12x – 15x2
+ 25x-20
= 6x4
– 10x3
+ 9x3
+ 8x2
– 15x2
– 15x2
+ 12x + 25x – 20
= 6x4
– x3
– 22x2
+ 37x – 20
Question 28.
(3x – 2) (2x – 3) + (5x – 3) (x + 1)
Solution:
(3x – 2) (2x – 3) + (5x – 3) (x + 1)
= 3x (2x – 3) -2 (2x – 3) + 5x (x + 1) – 3 (x + 1)
= 6x2
– 9x – 4x + 6 + 5x2
+ 5x – 3x – 3
= 6x2
+ 5x2
– 9x – 4x + 5x – 3x + 6 – 3
= 11x2
– 11x + 3
Question 29.
(5x – 3) (x + 2) – (2x + 5) (4x – 3)
Solution:
(5x – 3) (x + 2) – (2x + 5) (4x – 3)
= [5x (x + 2) -3 (x + 2)] – [2x (4x – 3) + 5 (4x – 3)]
= [5x2
+ 1 0x – 3x – 6] – [8x2
– 6x + 20x -15]
= (5x2
+ 7x – 6) – (8x2
+ 14x – 15)
= 5x2
+ lx – 6 – 8x2
– 14x + 15
= 5x2
– 8x2
+ 7x – 14x – 6 + 15
= -3x2
– 7x + 9
Question 30.
(3x + 2y) (4x + 3y) – (2x – y) (7x – 3y)
Solution:
(3x + 2y) (4x + 3y) – (2x – y) (7x – 3y)
= [3x (4x + 3y) + 2y (4x + 3y)]-[2x (7x-3y)-y(7x-3y)]
= (12x2
+ 9xy + 8xy + 6y2
) – (14x2
– 6xy – 7xy + 3y2
)
= (12x2
+ 17xy + 6y2
) – (14x2
– 13xy + 3y2
)
= 12x2
+ 17xy + 6y2
– 14x2
+ 13xy – 3y2
= 12x2
– 14x2
+ 17xy + 13xy + 6y2
– 3y2
= -2x2
+ 30xy + 3y2
= -2x2
+ 3y2
+ 30xy
Question 31.
(x2
-3x + 2) (5x- 2) – (3x2
+ 4x-5) (2x- 1)

11. Solution:
(x2
-3x + 2) (5x- 2) – (3x2
+ 4x-5) (2x- 1)
= [5x (x2
– 3x + 2) -2 (x2
– 3x + 2)] – [2x (3x2
+ 4x – 5) -1 (3x2
+ 4x – 5)]
= [5x3
– 15x2
+ 10x – 2x2
+ 6x – 4] – [6x3
+ 8x2
– 10x – 3x2
– 4x + 5]
= [5x3
– 15x2
– 2x2
+ 10xc + 6x – 4] – [6x3
+ 8x2
– 3x2
– 10x – 4x + 5]
= (5x3
– 17x2
+ 16x-4) – (6x3
+ 5x2
– 14x + 5)
= 5x3
– 17x2
+ 16x – 4 – 6x3
– 5x2
+ 14x – 5
= 5x3
– 6x3
– 17x2
– 5x2
+ 16x + 14x – 4 – 5
= -x3
– 22x2
+ 30x – 9
Question 32.
x3
– 2x2
+ 3x – 4) (x – 1) – (2x – 3) (x2
– x + 1)
Solution:
(x3
– 2x2
+ 3x – 4) (x – 1) – (2x – 3) (x2
– x + 1)
= [x (x3
– 2x2
+ 3x – 4) – 1 (x3
– 2x2
+ 3x – 4)] – [2x (x2
– x + 1) – 3 (x2
– x + 1)]
= [x4
– 2x3
+ 3x2
– 4x – x3
+ 2x2
– 3x + 4] [2x3
– 2x2
+ 2x – 3x2
+ 3x – 3]
= (x4
– 2x3
– x3
+ 3x2
+ 2x2
– 4x – 3x + 4) (2x3
– 2x2
– 3x2
+ 2x + 3x – 3)
= (x4
– 3x3
+ 5x2
– 7x + 4) – (2x3
– 5x2
+ 5x – 3)
= x4
– 3x3
+ 5x2
– 7x + 4 – 2x3
+ 5x2
– 5x + 3
= x4
– 3x3
– 2x3
+ 5x2
+ 5x2
– 7x – 5x + 4 + 3
= x4
– 5x3
+ 10x2
– 12x + 7