SIMPLIFYING POLYNOMIALS EXPRESSIONS BY COMBINING LIKE TERMS

To simplify polynomial expression, we need to know the terms Like and Unlike.

Like terms :

Like terms are terms that have the same variables with the same exponents.

Unlike terms :

Terms that are not like terms in unknown as unlike terms.

Write the sum or difference of the given polynomials in simplest form.

Problem 1 :

(3y - 5) + (2y - 8)

Solution :

= (3y - 5) + (2y - 8)

By combining like terms, we get

= 3y + 2y - 5 - 8

= 5y - 13

Problem 2 :

(x+ 3x - 2) + (4x-2x + 3)

Solution :

(x+ 3x - 2) + (4x- 2x + 3)

By combining like terms, we get

= x+ 4x2 + 3x - 2x - 2 + 3

= 5x+ x + 1

Problem 3 :

(4x- 3x - 7) + (3x- 2x + 3)

Solution :

= (4x- 3x - 7) + (3x- 2x + 3)

By combining like terms, we get

= 4x2 + 3x- 3x - 2x - 7 + 3

= 7x- 5x - 4

Problem 4 :

(-x+ 5x + 8) + (x- 2x - 8)

Solution :

(-x+ 5x + 8) + (x- 2x - 8)

By combining like terms, we get

= -x+ x+ 5x - 2x + 8 - 8

= 3x

Problem 5 :

(a2b- ab + 5) + (a2b2 + ab - 3)

Solution :

(a2b- ab + 5) + (a2b2 + ab - 3)

By combining like terms, we get

= a2b+ a2b- ab + ab + 5 - 3

= 2a2b+ 2

= 2(a2b+ 1)

Problem 6 :

(7b- 2b + 3) – (3b+ 8b + 3)

Solution :

(7b- 2b + 3) – (3b+ 8b + 3)

By combining like terms, we get

= 7b- 3b- 2b - 8b + 3 - 3

= 4b- 10b

By factoring 2b, we get

= 2b(2b - 5)

Problem 7 :

(3 + 2b + b2) – (9 + 5b + b2)

Solution :

(3 + 2b + b2) – (9 + 5b + b2)

= 3 - 9 + 2b - 5b + b- b2

= -6 - 3b

By factoring -3, we get

 = -3(2 + b)

Problem 8 :

(4x- 3x - 5) – (3x- 10x + 3)

Solution :

(4x- 3x - 5) – (3x- 10x + 3)

= 4x- 3x- 3x + 10x - 5 - 3

= x+ 7x - 8

Problem 9 :

(y- y - 7) + (3 - 2y + 3y2)

Solution :

(y- y - 7) + (3 - 2y + 3y2)

= y+ 3y- y - 2y - 7 + 3

= 4y- 3y - 4

Problem 10 :

(2a- 5a- 1) + (a+ a)

Solution :

(2a- 5a- 1) + (a+ a)

= 2a+ a- 5a+ a - 1

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