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# Addition and subtraction of Algebraic Expressions

Algebra

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Addition and Subtraction of Algebraic Expressions
a) 4a + 6b + 5c, -3a 9b , a + 3b 4c = 4a + 6b + 5c + (- 3a 9b ) + a + 3b - 4c
= 4a + 6b + 5c 3a 9b + a + 3b 4c
= 4a 3a + a +6b 9b + 3b +5c 4c
= 2a + c
b) p + 2q 4r, 2p 3q + 5r , 3p q + 2r = p + 2q 4r + 2p 3q +5r + 3p q + 2r
= p + 2p + 3p + 2q 3q q 4r +5r + 2r
= 6p 2q + 3r
c) 5x 4y , 6y 7z , 3z 4x = 5x 4y + 6y 7z + 3z x
= 5x 4x -4y +6y 7z + 3z
= x + 2y 4z
d) 9p + 12q 3r -4s, -8q + 4s, -7p + q +2r, p + 4r 5s = 9p+12q-3r -4s+(-8q+4s)+(-7p+q+2r)+p+4r-5s
=9p-12q-3r-4s-8q+4s-7p+q+2r+p+4r-5s
=9p-7p+p-12q-8q+q-3r+2r+4r-4s+4s-5s
= 3p+5q+3r-5s
Subtraction:
a) a 2b + 6c from 3a + 3b 4c = 3a + 3b 4c (a 2b + 6c)
= 3a + 3b -4c a + 2b 6c
= 3a a + 3b + 2b 4c 6c
= 2a + 5b -10c
b) 2q 3r s from p 4q 6r = p 4q 6r ( 2q 3r s )
= p 4q -6r 2q + 3r + s
= p 4q -2q 6r + 3r + s
= p 6q -3r + s
c) 8a 3b + 5c 2d from 10a b -4c -6d = 10a b 4c -6d (8a 3b + 5c -2d)
= 10 a b -4c 6d 8a + 3b 5c + 2d
= 10a -8a b +3b -4c -5c -6d + 2d
= 2a + 2b -9c 4d
d) 7p + 6q 5r from 10p 7q + 8r = 10p 7q + 8r (7p + 6q 5r)

= 10p -7q + 8r 7p 6q + 5r
= 10p 7p - 7q 6q + 8r + 5r
= 3p 13q + 13r
dd)

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