EXERCISE - A
Type- 1
1) ab and ab.
2) 2x and 3x.
3) 7y and -3y.
4) 3xyz and - 3xyz.
5) 2xy, - 3ab.
6) 9a² and -2a².
7) 5p/2 and -3p/2. p
Type -2
1) 4ab, -6ab, 3ab.
2) 12lx, -13my and 25nz.
3) 3lm, 7lm, -4lm.
4) 5x, -8x and 9x.
5) 5z², - 12z² and 19z².
6) 23x³, 12x³ and -34x³.
7) 2x²y, 4x²y, -6x²y.
Type- 3
1) 2a, 3a, 7a and 5a.
2) 3x, -5x, 8x and -2x.
3) 6a², 12a², - 9a² and - 15a².
5) 3xy, -2xy, - xy and -6xy.
6) 6mn, 4mn, - 2mn and 8mn.
7) 8a, 7b, - 3a and -5c.
8) 3abc, 4bcx, 2abcd, - 5abc.
9) xyz/2, xyz, 3xyz/2 and - 2xyz.
10) 6x, 13y, -4x, 9y, -3y and 16x.
EXERCISE - B
Type - 1
1) 2x + 3y and 5x - 3y .
2) 8x - 12y and 3y -7x.
3) 3m - 6n and 7n + 8m.
4) 7x+ 2y and -5x+8y.
Type - 2
1) a+ b +2 and a - b -1.
2) 5x²+ 2x +1 and x²+ x +3.
3) 9m²+ m +1 and - m²- 2m -3.
4) m²+ 2m +4 and -3m²-2m +4.
Type - 3
1) 3a- 7b, 5a+ 8b and -6a+ 9b.
2) 13x+12 y- 5z, 7x- 13y+ 16z and -6x+ 7y+12.
3) 3x+ 4y, 7x- 3y and -2x +8y.
4) 2a- 3b, 4a +6b and a +b.
5) 7x - 13y, 2x + y and 11x - 3y.
6) a- b, b - c and c -a .
7) 3a + 4b, 5a - 6 b, 8b + 9a.
8) 5x² -11x +4, 3x -11.
Type - 4
1) 6ax + 11by +17cz + 15, 8ax - 8cz +13.
2) x+ y - z, 3x - 6 y - 7z, 7x + 6y+8z.
3) 3x+ 2y- 5z, 7x- 3y+ 6z, -6x+ 2z.
4) x - y+ 2z, 3x - 6y- 7z and 8z - 3y+2x.
5) 2x + y -5, 7x -3 y+7 and 8x +12y+19.
6) 2ab +3bc + 6ca, 3ab - 5bc - 16ca and -5ab+ 2bc +10ca .
7) 7xy + 3yz - 5zx, -5xy -2yz +3zx and 8xy + 4yz +8zx.
8) x - 3y + 7z, 18x + 10y -11z and - 11x - 6y +2z.
9) 5x² +3x -8, 4x +7- 2x², 4x² -5x +6, 3x -11.
10) 3x² -4x +1, -4x²+5x +5, 2x² - 3x -2.
11) a² +5ab -7b² , 8a² -9ab -10b² and -17a² -10ab +18b² .
12) 8x²- 17xy + 24y², 16x²+23xy -41y², -11x²+42xy -50y².
13) 9x²- 11xy + 7y², - 5xy + 6y² - 3x, 11x²+7xy -5y².
14) 15m²n - 16 mn² + 18mn, -4m²n +17mn- 18 mn², 17m²n +3mn² -19mn.
Type - 5
1) 11a + 15b - 8c +7d, 10a +9c -13d, 9a + 8b - 11c -17d.
2) 4p²q - 3pq + 5pq²- 8p + 7q -10, 5p²q +5pq -2pq²- 3p -11q +18.
3) 5x³/3 + 3x + 6/5 + 3x², -7x³/3 + 8x + 4/5, -3x³/4 + 7x + 2/5 + 2x².
4) 5x³/3 + 3x + 6/5 + 3x², 2x²/3+ 5x³/3 + 8x - 4/3, -3 + 2x/3 + 5x³/2 - 5x²/3.
5) 3a⁴ - 4a² -5a -2 , -6a⁴ +2a² -8a +6 and 11a + 7a⁴+ 3+ 5a².
6) 1- 9x + 13x² - 12x³, 11x³+ 7x²- 4, 19x²- 3x - 24 and 6x³+ 21x.
7) 3a²- 6ab - 7b², 4b²- 3a²+ 7a +6b, 4ab - 3+ 2b + 5b² and 7 - 2b + a - 2ab.
Type - 6
1) a - b + c - 3d, 2a + 6b + 7c+ 8d, 5a + 6 b - 7c- 18d, - 9a+ 16b- 9c - 13d.
2) ax + by - 2cz, 4by - 7cz, 12ax - 5by +3cz and 10ax - 5cz.
3) 43a²--6a - 1, - 5a³ + 6 a²- 6 a+ 16, 7a³ + 13a²-9a +5, - 12a³+ 21a²+ 17a+4.
EXERCISE - C
Substraction
Type - 1
1) - 12 x y z from 0.
2) 2x from 5x. 3x
3) - 7x from 3x.
4) 2x from 4x.
5) - 3 l from 5 l .
6) 13yz from - 2yz.
7) z/3 from z/2.
8) 3z from 13x.
9) - 7b from 8a.
10) 5b from 8a.
11) x - y from y.
12) - 3 x² from -5x².
13) 7x²y from - 9x²y.
Type - 2
1) 11x - 13y from 15x- 8y.
2) 2a + 3b from 5a - 7b.
3) x²- y² from x² + y².
4) - 6x² + 3x from -8x²- 9.
Type - 3
1) 7x + 8y - 9z from 11x - 2y - 13z.
2) 3x -2y - z from 4x - 3y +5z.
3) 4x + 5y - 8z from 12x - 7y - 6z.
4) 2x - 3y + 4z from 7x + 5y + 9z.
5) 5a + 3b - 4c from 11a - b - c.
6) - 3ab+ 4bc -6ca from 2ab+13bc+ 6ca.
7) - 5 x² + 2x + 1 from x² - x - 5.
8) 3a²- 2b² - 7c² from 11a² + 17b² - 9c².
9) 12 x² + 3y² - 11z² from 7x² - 9y² - 11z².
10) a²b - 4ab²/5 + 4ab/3 from 2a²b/3 +3ab²/2 - ab/3.
Type - 4
1) 7a + 18b +19c - 5d from 12a + 36b - 8c+ 9d.
2) 8xy - 5yz + 3xz +21 from 6xy +9yz -7xz + 17.
3) 6 a² +12ab - 7b² from - 8a²+ 10ab - 5b².
4) x²+ x +1 from x²- x +1.
5) a²+ 2a - 3 from 3a²- 2a +4.
6) - 7x² - 3xy + 8y² from 4x² - 3xy - 2y².
7) 3x² - 6x - 4 from + 5 + x - 2x².
8) 3x⁴y² - 7x²y + 4 x y from -2x⁴y + 5 x³ y² - 3x²y.
Type - 5
1) 4p² + 5q² - 6r²+ 7 from 3p²q -4q² - 5r²-10.
2) a³+ b³+ c³ - 3abc from 7abc -3a³+ 5b³- c³.
3) 5x⁴ + 4 x² -3x + 2 from 13x⁴ - 7x²+ 6x - 7.
4) 5 x⁴- 6x³y+ 7x²y²- 8xy² - 19y⁴ from 3x⁴ + 5 x² y² - 12y⁴.
5) 8x⁴ - 7x³ + 5x²- 6x from- 10x⁴ + 5 x³ + 2x² - 4 x.
6) 4p²q - 3pq + 5pq²- 8p + 7q -10 from 18 -3p -11q +5pq -2pq² + 5p²q.
7) 6x²y - 4xy + 7xy²- 8x + 9y -11 from 19 -3x - 15y + 7xy - 2xy² + 3x²y.
EXERCISE - D
SIMPLIFY THE FOLLOWING :
a) 9a + 3a - 2a + 11a.
b) 5ab + 16cd + 11ab - 12 ab -3cd - a b + 7cd. 3ab+ 10cd
c) 7 + 5 a²b - 6ab² + 9 + 3ab² - 2a²b - 12 + 15ab². 4+ 3a²b + 12ab²
d) 8a + 3b - 7c - 7a + 2b- 3c+ 9c - b. 12a + 4b - c
EXERCISE - E
1) How much larger is 11x³ -5x² + 3 than 6x³ + 7x.
2) How much smaller is 5a² - 7abb + 9 b² than 8a²- 4b²?
3) How much should be subtracted from 3ab - 4bc + abc to get 2ab + 3abc + 1?
4) How much should be added to 8y³ - 3y -4 to get y²+ y+ 1?
5) What should be added to 6x³ - 5 x y² + 3 to get -9x³ + 7 x² y + 9 ?
6) What must be added to them to the sum of x+ 3 y and x - 5y so that the resulting sum is 5x - 2y ?
7) What must be added to 10a²b+ 8ab - 8a³b³ - b⁴ to get 5a²b - 6ab² - 7a³b³.
8) ) Subtract 2xy - a² - b² from x² - 2 xy + y², and from the remainder(i.e., the difference) obtained, subtract x²+ y²+ a²+ b².
9) Subtract 2xy - a²- b² from x²- 2xy + y², and from the sum 3a² - 5ax -x² and -2a² + 3ax + 4 x².
10) The difference of two algebraic expressions is -15a³ + 8a² - 5a + 3, if the larger one is 20a³ 10a²+ 6a - 6, find the smaller one. 35a³+ 2a²+ 11a - 9
11) Find the expression that must be subtracted from 6a² - 7a - 8 to get 3a² + 7a + 1.
12) The sum of two algebraic expressions is 36a⁴ - 22a³b + 27ab²- b³. One of them is 2b³+ 17a⁴ - 13 a³b. Find the other.
13) From the sum of 11o + 9q - 7r and -7p -12q + 8r, subtract the sum of 6p + 14q- 13r and 15p - q + 12r.
14) The sum of the two expressions is a - b - 7c + 9. If one of them is 3a + 4b -8c - 11. find the other.
15) The perimeter of a triangle is 6p²- 4p +9 and two of its sides p²- 2p +1 and 3p²- 5p +3. Find the third side of the triangle.
16) The perimeter of a triangle is 14p- 3q +12 r. If two of its sides 4p + 6q -8r and 3p- 5q +11r. Find the third side of the triangle.
17) Two adjacent sides of a rectangle are 5a² - 2b and 4a²+ 3b. Find its perimeter.
18) The two sides of a triangle are (5x + 1)cm and (x²- 5 x-4)cm. If its perimeter is (3x²+ 4x +2)cm, find the length of its third side.
19) A man divides Rs(7x³ + 2 x² y +4y) among his two sons. If one of them gets Rs(5x³ + 2y - 4), how much does the other one get ?
20) A man walks to 2a - b km due North from a fixed point O and then walks a distance of 3a + 2b km due South. What is his final position regard to O.
21) There are (10a + 13b) passengers on a train. If (4a - 3b) and (5b - 2 a) passengers board at two consecutive stations, what is the number of passengers on the train now.
22) A stick is cut into three pieces of lengths (7x - 2y + 3z)cm, (y - 3x + 7z)cm and (z - 3y + x) cm. Find the original length of the sticks.
23) Ram has Rs(16a- 3b) with him. If he spends Rs(2a+ b), how much money is left with him.
EXERCISE - F
Multiplication
Type - 1
1) 2 by - 4x.
2) - 5 by - 6a.
3) 7 by - 13x².
4) 4x by 3.
5) 8x by -2.
6) - 12p by 2.
7) - 9y by -5.
8) 7 x² by - 2.
9) - 8y by - 12y.
10) - 3 x by 4y.
11) 80x by -5y.
12) 9m by -6n.
13) - 12p by 7q.
Type - 2
1) (x + 5) by 2.
2) 3a -4 by -3.
3) -7p + 8 by 3.
4) 8p - 9q by 11.
5) 18 k + 13m by - 2.
6) -17p + 18a by 2.
7) - 3 x - 8 by 5.
8) -8m - 9n by -6.
9) 2x - 5t by 2 x.
10) 3x + 7y by - 3x.
11) -8a + 9b by 3a.
12) 2x - 3y by -6z.
13) - 3x - 2y by 7x.
14) 9l - 9m by 4m.
15) 18x +13y by 7y.
16) - 2A - 3b by -4a.
17) 7a - 2b by -3x.
18) -12a + 6x by 7c.
19) 0.2a + 1.5b by -4z.
Type- 4
1) 2(6x +5).
2) 7(3x -4).
3) 2a(-7a +5).
4) -5x(-6x - 7y).
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