Selina solutions

Selina solutions

Grade 6

Fundamental Operations (Related to Algebraic Expressions) | Exercise 19(B)

Question 1

Q1) Find the sum of:

(i) 3a+4b+7c, -5a+3b-6c and 4a-2b-4c

(ii) 2x^2+xv-y^2,\ -x^2+2xy+3y^{2\ }and\ 3x^2-10xy+4y^2

(iii) x^2-x+1,\ -5x^2+2x-2\ and\ 3x^2-3x+1

(iv) a^2-ab+bc,\ 2ab+bc-2a^2\ and\ -3bc+3a^2+ab

(v) 4x^2+7-3x,\ 4x-x^2+8\ and\ -10+5x-2x^2

(vi) 3x+4xy-y^2,\ xy-4x+2y^2\ and\ 3y^2-xy+6x

Solution 1:

(i) (3a+4b+7c) + (-5a+3b-6c) + (4a-2b-4c)

= 3a+4b+7c-5a+3b-6c+4a-2b-4c

= 3a+4a-5a+4b+3b-2b+7c-6c-4c

= 7a-5a+7b-2b+7c-10c

= 2a+5b-3c

(ii) \left(2x^2+xy-y^2\right)+\left(-x^2+2xy+3y^2\right)+\left(3x^2-10xy+4y^2\right)

=2x^2+xy-y^2-x^2+2xy+3y^2+3x^2-10xy+4y^2

=2x^2+3x^2-x^2+xy+2xy-10xy+3y_{ }^2+4y^2-y^2

=5x^2-x^2+3xy-10xy+7y^2-y^2

=4x^2-7xy+6y^2

(iii) \left(x^2-x+1\right)+\left(-5x^2+2x-2\right)+\left(3x^2-3x+1^{ }\right)

=x^2+3x^2-5x^2+2x-x-3x+1+1-2

=4x^2-5x^2+2x-4x+2-2=-x^2-2x

(iv) \left(a^2-ab+bc\right)+\left(2ab+bc-2a^2\right)+\left(-3bc+3a^2+ab\right)

=a^2-ab+bc+2ab+bc-2a^2-3bc+3a^2+ab

=a^2+3a^2-2a^2+2ab+ab-ab+bc+bc-3bc=4a^2-2a^2+3ab-ab+2bc-3bc

2a^2+2ab-bc

(v) \left(4x^2+7-3x\right)+\left(4x-x^2+8\right)+\left(-10+5x-2x^2\right)

=4x^2+7-3x+4x-x^2+8-10+5x-2x^2

4x^2-x^2-2x^2+7+8-10+4x+5x-3x=4x^2-3x^2+15-10+9x-3x

=x^2+5+6x

(vi) \left(3x+4xy-y^2\right)+\left(xy-4x+2y^2\right)+\left(3y^2-xy+6x\right)

=3x+4xy-y^2+xy-4x+2y^2+3y^2-xy+6x

=3x+6x-4x+4xy+xy-xy+2y^2+3y^2-y^2

=9x-4x+5xy-xy+5y^2-y^2

=5x+4xy+4y^2

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Question 1

Q1) Find the sum of:

(i) 3a+4b+7c, -5a+3b-6c and 4a-2b-4c

(ii) 2x^2+xv-y^2,\ -x^2+2xy+3y^{2\ }and\ 3x^2-10xy+4y^2

(iii) x^2-x+1,\ -5x^2+2x-2\ and\ 3x^2-3x+1

(iv) a^2-ab+bc,\ 2ab+bc-2a^2\ and\ -3bc+3a^2+ab

(v) 4x^2+7-3x,\ 4x-x^2+8\ and\ -10+5x-2x^2

(vi) 3x+4xy-y^2,\ xy-4x+2y^2\ and\ 3y^2-xy+6x

Solution 1:

(i) (3a+4b+7c) + (-5a+3b-6c) + (4a-2b-4c)

= 3a+4b+7c-5a+3b-6c+4a-2b-4c

= 3a+4a-5a+4b+3b-2b+7c-6c-4c

= 7a-5a+7b-2b+7c-10c

= 2a+5b-3c

(ii) \left(2x^2+xy-y^2\right)+\left(-x^2+2xy+3y^2\right)+\left(3x^2-10xy+4y^2\right)

=2x^2+xy-y^2-x^2+2xy+3y^2+3x^2-10xy+4y^2

=2x^2+3x^2-x^2+xy+2xy-10xy+3y_{ }^2+4y^2-y^2

=5x^2-x^2+3xy-10xy+7y^2-y^2

=4x^2-7xy+6y^2

(iii) \left(x^2-x+1\right)+\left(-5x^2+2x-2\right)+\left(3x^2-3x+1^{ }\right)

=x^2+3x^2-5x^2+2x-x-3x+1+1-2

=4x^2-5x^2+2x-4x+2-2=-x^2-2x

(iv) \left(a^2-ab+bc\right)+\left(2ab+bc-2a^2\right)+\left(-3bc+3a^2+ab\right)

=a^2-ab+bc+2ab+bc-2a^2-3bc+3a^2+ab

=a^2+3a^2-2a^2+2ab+ab-ab+bc+bc-3bc=4a^2-2a^2+3ab-ab+2bc-3bc

2a^2+2ab-bc

(v) \left(4x^2+7-3x\right)+\left(4x-x^2+8\right)+\left(-10+5x-2x^2\right)

=4x^2+7-3x+4x-x^2+8-10+5x-2x^2

4x^2-x^2-2x^2+7+8-10+4x+5x-3x=4x^2-3x^2+15-10+9x-3x

=x^2+5+6x

(vi) \left(3x+4xy-y^2\right)+\left(xy-4x+2y^2\right)+\left(3y^2-xy+6x\right)

=3x+4xy-y^2+xy-4x+2y^2+3y^2-xy+6x

=3x+6x-4x+4xy+xy-xy+2y^2+3y^2-y^2

=9x-4x+5xy-xy+5y^2-y^2

=5x+4xy+4y^2

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