Q1: If P = 2x2 - 5x + 2, Q = 5x2 + 6x - 3 and R = 3x2 - x - 1. Find the value of 2P - Q + 3R.
Sol: 2P - Q + 3R = 2(2x2 - 5x + 2) - (5x2 + 6x - 3) + 3(3x2 - x - 1)
= 4x2 - 10x + 4 - 5x2 - 6x + 3 + 9x2 - 3x - 3
= 4x2 - 5x2 + 9x2 - 10x - 6x - 3x + 4 + 3 - 3
= 8x2 - 19x + 4
Required expression.
Q2: If A = -(2x + 3), B = -3(x - 2) and C = -2x + 7. Find the value of k if (A + B + C) = kx.
Sol: A + B + C = -(2x + 13) - 3(x - 2) + (-2x + 7)
= -2x - 13 - 3x + 6 - 2x + 7
= -2x - 3x - 2x - 13 + 6 + 7
= -7x
Since A + B + C = kx
-7x = kx
Thus, k = -7
Q3: Rohan's mother gave him ₹ 3xy2 and his father gave him ₹ 5(xy2 + 2). Out of this total money he spent ₹ (10 - 3xy2) on his birthday party. How much money is left with him? [NCERT Exemplar]
Sol: Money give by Rohan's mother = ₹ 3xy2
Money given by his father = ₹ 5(xy2 + 2)
Total money given to him = ₹ 3xy2 + ₹ 5 (xy2 + 2)
= ₹ [3xy2 + 5(xy2 + 2)]
= ₹ (3xy2 + 5xy2 + 10)
= ₹ (8xy2 + 10).
Money spent by him = ₹ (10 - 3xy)2
Money left with him = ₹ (8xy2 + 10) - ₹ (10 - 3xy2)
= ₹ (8xy2 + 10 - 10 + 3x2y)
= ₹ (11xy2)
Hence, the required money = ₹ 11xy2
Q4: Add: 5x-8y+2z,3z-4y-2x,6y-z-x and 3x-2z-3y.
Sol: Let us add the given expressions 5x-8y+2z,3z-4y-2x,6y-z-x and 3x-2z-3y as shown below:
(5x-8y+2z)+(3z-4y-2x)+(6y-z-x)+(3x-2z-3y)
=5x-8y+2z+3z-4y-2x+6y-z-x+3x-2z-3y
=(5x-2x-x+3x)+(-8y-4y+6y-3y)+(2z+3z-z-2z)(Combiningliketerms)
=(5-2-1+3)x+(-8-4+6-3)y+(2+3-1-2)z
=5x-9y+2z
Hence, (5x-8y+2z)+(3z-4y-2x)+(6y-z-x)+(3x-2z-3y)=5x-9y+2z.
Q5: Add: (4x2 -7xy+4y2 -3),(5+6y2 -8xy+x2) and (6-2xy+2x2 -5y2).
Sol: Let us add the given expressions 4x2 -7xy+4y2 -3,5+6y2 -8xy+x2 and 6-2xy+2x2 -5y2 as shown below:
(4x2 -7xy+4y2 -3)+(5+6y2 -8xy+x2)+(6-2xy+2x2 -5y2)
=4x2 -7xy+4y2 -3+5+6y2 -8xy+x2 +6-2xy+2x2 -5y2
=(4x2 +x2 +2x2)+(-7xy-8xy-2xy)+(4y2 +6y2 -5y2)+(-3+5+6)(Combiningliketerms)
=(4+1+2)x2 +(-7-8-2)xy+(4+6-5)y2 +8
=7x2 -17xy+5y2 +8
Hence, (4x2 -7xy+4y2 -3)+(5+6y2 -8xy+x2)+(6-2xy+2x2 -5y2)
=7x2 -17xy+5y2 +8.
Q6: Subtract4a+3b from 2a+2b-4.
Sol: Let us subtract the given expression 4a+3b from 2a+2b-4 as shown below:
(2a+2b-4)-(4a+3b)
=2a+2b-4-4a-3b
=(2a-4a)+(2b-3b)-4(Combiningliketerms)
=(2-4)a+(2-3)b-4
=-2a-b-4
Hence, (2a+2b-4)-(4a+3b)=-2a-b-4.
Q7: Simplify 2(3b-5a)-7[9-62-5(a-6)]
Sol:
=2(3b-5a)-7[9-62-5(a-6)]
=6b-10a-(63-434-35(a-6))
=6b-10a-(63-434-35a-210)
=6b-10a-63+434+35a+210
=25a+6b+581.
Q8: Add: 6p+4q-r+2r-5p-6,11q-7p+2r-1 and 2q-3r+4.
Sol: Let us add the given expressions 6p+4q-r+2r-5p-6,11q-7p+2r-1 and 2q-3r+4 as shown below:
(6p+4q-r)+(2r-5p-6)+(11q-7p+2r-1)+(2q-3r+4)
=6p+4q-r+2r-5p-6+11q-7p+2r-1+2q-3r+4
=(6p-5p-7p)+(4q+11q+2q)+(-r+2r+2r-3r)+(-6-1+4)(Combiningliketerms)
=(6-5-7)p+(4+11+2)q+(-1+2+2-3)r-3
=-6p+17q-3
Hence, (6p+4q-r)+(2r-5p-6)+(11q-7p+2r-1)+(2q-3r+4)=-6p+17q-3.
