SIMPLIFYING POLYNOMIALS EXPRESSIONS BY COMBINING LIKE 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 :

(x² + 3x - 2) + (4x² -2x + 3)

Solution :

= (x² + 3x - 2) + (4x² - 2x + 3)

By combining like terms, we get

= x² + 4x² + 3x - 2x - 2 + 3

= 5x² + x + 1

Problem 3 :

(4x² - 3x - 7) + (3x² - 2x + 3)

Solution :

= (4x² - 3x - 7) + (3x² - 2x + 3)

By combining like terms, we get

= 4x² + 3x² - 3x - 2x - 7 + 3

= 7x² - 5x - 4

Problem 4 :

(-x² + 5x + 8) + (x² - 2x - 8)

Solution :

= (-x² + 5x + 8) + (x² - 2x - 8)

By combining like terms, we get

= -x² + x² + 5x - 2x + 8 - 8

= 3x

Problem 5 :

(a²b² - ab + 5) + (a²b² + ab - 3)

Solution :

= (a²b² - ab + 5) + (a²b² + ab - 3)

By combining like terms, we get

= a²b² + a²b² - ab + ab + 5 - 3

= 2a²b² + 2

= 2(a²b² + 1)

Problem 6 :

(7b² - 2b + 3) – (3b² + 8b + 3)

Solution :

= (7b² - 2b + 3) – (3b² + 8b + 3)

By combining like terms, we get

= 7b² - 3b² - 2b - 8b + 3 - 3

= 4b² - 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 + b² - b²

= -6 - 3b

By factoring -3, we get

 = -3(2 + b)

Problem 8 :

(4x² - 3x - 5) – (3x² - 10x + 3)

Solution :

= (4x² - 3x - 5) – (3x² - 10x + 3)

= 4x² - 3x² - 3x + 10x - 5 - 3

= x² + 7x - 8

Problem 9 :

(y² - y - 7) + (3 - 2y + 3y²)

Solution :

= (y² - y - 7) + (3 - 2y + 3y²)

= y² + 3y² - y - 2y - 7 + 3

= 4y² - 3y - 4

Problem 10 :

(2a⁴ - 5a² - 1) + (a³ + a)

Solution :

= (2a⁴ - 5a² - 1) + (a³ + a)

= 2a⁴ + a³ - 5a² + a - 1

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