SIMPLIFY BY COMBINING LIKE TERMS

Simplify combining like terms :

Problem 1 :

21b – 32 + 7b – 20b

Solution :

21b – 32 + 7b – 20b

Combine the like terms,

= (21b + 7b - 20b) - 32

= 8b - 32

Problem 2 :

–z² + 13z² – 5z + 7z³ – 15z

Solution :

–z² + 13z² – 5z + 7z³ – 15z

Group the like terms,

= (7z³) + (-z² + 13z²) + (-5z – 15z)

Combine the like terms,

= 7z³ + 12z² – 20z

Problem 3 :

p – (p – q) – q – (q – p)

Solution :

p – (p – q) – q – (q – p)

= p – p + q – q – q + p

= p - q

Problem 4 :

3a – 2b – ab – (a – b + ab) + 3ab + b – a

Solution :

3a – 2b – ab – (a – b + ab) + 3ab + b – a

= 3a – 2b – ab – a + b – ab + 3ab + b – a

Group the like terms,

= (3a – a – a) + (– 2b + b + b) + (– ab – ab + 3ab)

Combine the like terms,

= a + ab

Problem 5 :

5x²y – 5x² + 3yx² – 3y² + x² – y² + 8xy² – 3y²

Solution :

5x²y – 5x² + 3yx² – 3y² + x² – y² + 8xy² – 3y²

Group the like terms,

= (5x²y + 3yx²) + (– 5x² + x²) + (8xy²) + (- 3y²– y² – 3y²)

Combine the like terms,

= 8x²y – 4x² + 8xy² – 7y²

Problem 6 :

(3y² + 5y – 4) – (8y – y² – 4)

Solution :

= (3y² + 5y – 4) – (8y – y² – 4)

= 3y² + 5y – 4 – 8y + y² + 4

Group the like terms,

= (3y² + y²) + (5y – 8y) + (-4 + 4)

Combine the like terms,

= 4y² – 3y

Add the following :

Problem 1 :

3mn, -5mn, 8mn, -4mn

Solution :

= 3mn, -5mn, 8mn, -4mn

= 3mn + (-5mn) + 8mn + (-4mn)

= 11mn – 9mn

= 2mn

Problem 2 :

t – 8tz, 3tz – z, z - t

Solution :

= t – 8tz, 3tz – z, z - t

= t – 8tz + 3tz – z + z – t

= – 5tz

Problem 3 :

-7mn + 5, 12mn + 2, 9mn – 8, -2mn - 3

Solution :

Given, -7mn + 5, 12mn + 2, 9mn – 8, -2mn - 3

= -7mn + 5 + 12mn + 2 + 9mn – 8 + (-2mn – 3)

= -7mn + 5 + 12mn + 2 + 9mn – 8 – 2mn – 3

= -7mn + 12mn + 9mn – 2mn + 5 + 2 – 8 - 3

= 12mn - 4

Problem 4 :

a + b – 3, b – a + 3, a – b + 3

Solution :

= a + b – 3, b – a + 3, a – b + 3

= a + b – 3 + b – a + 3 + a – b + 3

= a – a + a + b + b – b – 3 + 3 + 3

= a + b + 3

Subtract the following :

Problem 1 :

-5y² from y²

Solution :

-5y² from y²

= y² – (-5y²)

= y² + 5y²

= (1 + 5)y²

= 6y²

Problem 2 :

6xy from -12xy

Solution :

6xy from -12xy

= -12xy – 6xy

= -18xy

Problem 3 :

(a – b) from (a + b)

Solution :

(a – b) from (a + b)

= a + b – (a – b)

= a + b – a + b

= 2b

Problem 4 :

a(b – 5) from b(5 – a)

Solution :

a(b – 5) from b(5 – a)

= b(5 – a) – a(b – 5)

= 5b – ab – ab + 5a

= 5a + 5b – ab – ab

= 5(a + b) – 2ab

Problem 5 :

-m² + 5mn from 4m² – 3mn + 8

Solution :

-m² + 5mn from 4m² – 3mn + 8

= 4m² – 3mn + 8 – (-m² + 5mn)

= 4m² – 3mn + 8 + m² – 5mn

= 4m² + m² – 3mn – 5mn + 8

= 5m² – 8mn + 8