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Algebraic Expressions

Question
CBSEENMA7000997
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Simplify combining like terms:

(i) 21b − 32 + 7b − 20b

(ii) − z2 + 13z2 − 5z + 7z3 − 15z

(iii) p − (p − q) − q − (q − p)

(iv) 3a − 2b − ab − (a − b + ab) + 3ab + b − a

(v) 5x2y − 5x2 + 3y x2 − 3y2 + x2 − y2 + 8xy2 −3y2

(vi) (3 y2 + 5y − 4) − (8y − y2 − 4)

Solution

(i) 21b − 32 + 7b − 20b = 21b + 7b − 20b − 32

= b (21 + 7 − 20) −32

= 8b − 32

(ii) − z2 + 13z2 − 5z + 7z3 − 15z = 7z3 − z2 + 13z2 − 5z − 15z

= 7z3 + z2 (−1 + 13) + z (−5 − 15)

= 7z3 + 12z2 − 20z

(iii) p − (p − q) − q − (q − p) = p − p + q − q − q + p

= p − q

(iv) 3a − 2b − ab − (a − b + ab) + 3ba + b − a

= 3a − 2b − ab − a + b − ab + 3ab + b − a

= 3a − a − a − 2b + b + b − ab − ab + 3ab

= a (3 − 1 − 1) + b (− 2 + 1 + 1) + ab (−1 −1 + 3)

= a + ab

(v) 5x2y − 5x2 + 3yx2 − 3y2 + x2 − y2 + 8xy2 − 3y2

= 5x2y + 3yx2 − 5x2 + x2 − 3y2 − y2 − 3y2 + 8xy2

= x2y (5 + 3) + x2 (−5 + 1) + y2(−3 − 1 − 3) + 8xy2

= 8x2y − 4x2 − 7y2 + 8xy2

(vi) (3y2 + 5y − 4) − (8y − y2 − 4)

= 3y2 + 5y − 4 − 8y + y2 + 4

= 3y2 + y2 + 5y − 8y − 4 + 4

= y2 (3 + 1) + y (5 − 8) + 4 (1 − 1)

= 4y2 − 3y

Some More Questions From Algebraic Expressions Chapter

Add:

(i) 3mn, − 5mn, 8mn, −4mn

(ii) t − 8tz, 3tz − z, z − t

(iii) − 7mn + 5, 12mn + 2, 9mn − 8, − 2mn − 3

(iv) a + b − 3, b − a + 3, a − b + 3

(v) 14x + 10y − 12xy − 13, 18 − 7x − 10y + 8xy, 4xy

(vi) 5m − 7n, 3n − 4m + 2, 2m − 3mn − 5

(vii) 4x2y, − 3xy2, − 5xy2, 5x2y

(viii) 3p2q2 − 4pq + 5, − 10p2q2, 15 + 9pq + 7p2q2

(ix) ab − 4a, 4b − ab, 4a − 4b

(x) x2 − y2 − 1 , y2 − 1 − x2, 1− x2 − y2

Subtract:

(i) − 5y2 from y2

(ii) 6xy from − 12xy

(iii) (a − b) from (a + b)

(iv) a (b − 5) from b (5 − a)

(v) − m2 + 5mn from 4m2 − 3mn + 8

(vi) − x2 + 10x − 5 from 5x − 10

(vii) 5a2 − 7ab + 5b2 from 3ab − 2a2 −2b2

(viii) 4pq − 5q2 − 3p2 from 5p2 + 3q2 − pq

(a) What should be added to x2 + xy + y2 to obtain 2x2 + 3xy?

(b) What should be subtracted from 2a + 8b + 10 to get − 3a + 7b + 16?

What should be taken away from 3x2 − 4y2 + 5xy + 20 to obtain

− x2 − y2 + 6xy + 20?

(a) From the sum of 3x − y + 11 and − y − 11, subtract 3x − y − 11.

(b) From the sum of 4 + 3x and 5 − 4x + 2x2, subtract the sum of 3x2 − 5x and − x2 + 2x + 5.

If p = −2, find the value of:

(i) 4p + 7

(ii) −3p2 + 4p + 7

(iii) −2p3 − 3p2 + 4p + 7

Find the value of the following expressions, when x = − 1:

(i) 2x − 7 (ii) − x + 2 (iii) x2 + 2x + 1

(iv) 2x2 − x − 2

If a = 2, b = − 2, find the value of:

(i) a2 + b2 (ii) a2 + ab + b2 (iii) a2 − b2

When a = 0, b = − 1, find the value of the given expressions:

(i) 2a + 2b (ii) 2a2 + b2 + 1

(iii) 2a2 b + 2ab2 + ab (iv) a2 + ab + 2

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