Worksheet on addition of polynomial with solution

Q.1 Add

(i) 41x²-6xy+12y²  and 11x²+2xy-7y² 

(ii) 9x²-10xy-5xy² ,3x²+15xy-2xy²  and -2x²+3xy²-2xy 

Q.2 What should be added to 12x²+3x-2 to obtain 3x² +9x+5 ? 

Q.3 Subtract the sum of 4x²-3xy+y² and -2xy +9x²-5y² from -8x²+5xy 

Q.4 Find the sum of 5x²-7xy+4y²-3x, 4x²+2xy-y², and x²+5xy-2y² +3x-y 

Q.5 What must be added to x² +4x -6 to get x³ -x²+2x-2? 

Solution 

Problem : 01

Add

(i) 41x²-6xy+12y²  and 11x²+2xy-7y² 

(ii) 9x²-10xy-5xy² ,3x²+15xy-2xy²  and -2x²+3xy²-2xy 

Solution: 

Note: For adding polynomial,we only the coefficients of like term 

(i) (41x²-6xy+12y²)+(11x²+2xy-7y² )

= 41x²+11x²-6xy+2xy+12y²-7y²

=52x²-4xy+5y²

(ii) 9x²-10xy-5xy² ,3x²+15xy-2xy²  and -2x²+3xy²-2xy 

(9x²-10xy-5xy²)+(3x²+15xy-2xy²)+(-2x²+3xy²-2xy)

= 9x²-10xy-5xy²+3x²+15xy-2xy²-2x²+3xy²-2xy

= 9x²+3x²-2x²-10xy+15xy-5xy²-2xy²+3xy²

= 10x²+3xy-4xy²

Problem : 02 

What should be added to 12x²+3x-2 to obtain 3x² +9x+5? 

Solution: 

Let Required algebraic expression is X 

12x²+3x-2+X=3x² +9x+5

X=(3x² +9x+5)-(12x²+3x-2) 

X=3x² +9x+5-12x²-3x+2 

X=-9x²+6x+7 

Problem: 03 Subtract the sum of 4x²-3xy+y² and -2xy +9x²-5y² from -8x²+5xy 

Solution: Sum of 4x²-3xy+y² and -2xy +9x²-5y²

(4x²-3xy+y²)+(-2xy +9x²-5y²)=4x²-3xy+y²-2xy+9x²-5y²

=13x²-5xy-4y²

Subtract 13x²-5xy-4y² from -8x²+5xy 

(-8x²+5xy )-(13x²-5xy-4y²) 

= -8x²+5xy-13x²+5xy+4y²

=-21x²+10xy+4y²

Problem: 04 What must be added to x² +4x -6 to get x³ -x²+2x-2? 

Solution: 

Let required algebraic expression is X 

(x² +4x -6)+X=( x³ -x²+2x-2) 

x² +4x -6+X=x³ -x²+2x-2

X=(x³ -x²+2x-2)-(x² +4x -6) 

X=x³ -x²+2x-2-x²-4x+6 

X=x³-2x²-2x+4 

Check these resources as well 

 

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