S.chand publication New Learning Composite mathematics solution of class 8 Chapter 5 Algebraic Expressions Exercise 5D

 Exercise 5D

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Q1 | Ex-5D | Class 8 |Algebraic Expressions | S.chand  |New Learning Composite maths |myhelper

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Question 1

(a) (y – 6) (2y + 7)

Sol :

=y(2y+7)-6(2y+7)

=2y²+7y-12y-42

=2y²-5y-42

(b) (3x -7) (5x – 8)

Sol :

=3x(5x-8)-7(5x-8)

=15x²-24x-35x+56

=15x²-59x+56

(c) (x – 2) (6x + 9)

Sol :

=x(6x+9)-2(6x+9)

=6x²+9x-12x-18

=6x²-3x-18

(d) (3m² – n) (m² – 2n)

Sol :

=3m²(m²-2n)-n(m²-2n)

=3m⁴-6m²n-m²n+2n²

=3m⁴-7m²n+2n²

(e) (3a – b²) (2a + 7b²)

Sol :

=3a(2a+7b²)-b²(2a+7b²)

=6a²+21ab²-2ab²-7b⁴

=6a²+19ab²-7b⁴

(f) (x² – 2xy) (3xy + y²)

Sol :

=x²(3xy+y²)-2xy(3xy+y²)

=3x³y+x²y²-6x²y²-2xy³

=3x³y-5x²y²-2xy³

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Q2 | Ex-5D | Class 8 |Algebraic Expressions | S.chand  |New Learning Composite maths |myhelper

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Question 2

(a) (x – 2) (x² – 3x + 2)

Sol :

=x(x²-3x+2)-2(x²-3x+2)

=x³-3x²+2x-2x²+6x-4

=x³-5x²+8x-4

(b) (3x + 4) (x² – 5x + 2)

Sol :

=3x(x²-5x+2)+4(x²-5x+2)

=3x³-15x²+6x+4x²-20x+8

=3x³-11x²-14x+8

(c) (3 – y) (5y² – 2 – 3y)

Sol :

=3(5y²-2-3y)-4(5y²-2-3y)

=15y²-6-9y-5y³+2y+3y²

=-5y³+18y²-7y-6

(d) (4a – 3) (3a² + 2 – 5a)

Sol :

=4a(3a²+2–5a)-3(3a²+2–5a)

=12a³+8a-20a²-9a²-6+15a

=12a³+23a-29a²-6

=12a³-29a²+23a-6

(e) (5x – 1) (-2x³ + 4x – 3)

Sol :

=5x(-2x³+4x–3)-1(-2x³+4x–3)

=-10x⁴+20x²-15x+2x³-4x+3

=-10x⁴+20x²+2x³-19x+3

=-10x⁴+2x³+20x²-19x+3

(f) (2p² – 3) (4p³– p²+7)

Sol :

=2p²(4p³– p²+7)-3(4p³– p²+7)

=8p⁵-2p⁴+14p²-12p³+3p²-21

=8p⁵-2p⁴-12p³+17p²-21

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Q3 | Ex-5D | Class 8 |Algebraic Expressions | S.chand  |New Learning Composite maths |myhelper

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Question 3

(a) (x + 1) (x²–x+1)

Sol :

=x(x²–x+1)+1(x²–x+1)

=x³-x²+x+x²-x+1

=x³-1

(b) (x – y) (x²+xy+y²)

Sol :

=x(x²+xy+y²)-y(x²+xy+y²)

=x³+x²y+xy²-x²y-xy²-y³

=x³-y³

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Q4 | Ex-5D | Class 8 |Algebraic Expressions | S.chand  |New Learning Composite maths |myhelper

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Question 4

(a) (x³–5x²+2) (x²–2x)

Sol :

=x²(x³–5x²+2)-2x(x³–5x²+2)

=x⁵-5x⁴+2x²-2x⁴+10x³-4x

=x⁵-7x⁴+10x³+2x²-4x

(b) (2x²–3x+4) (x²–5x–3)

Sol :

=2x²(x²–5x–3)-3x(x²–5x–3)+4(x²–5x–3)

=2x⁴-10x³-6x²-3x³+15x²+9x+4x²-20x-12

=2x⁴-13x³+13x²-11x-12

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Q5 | Ex-5D | Class 8 |Algebraic Expressions | S.chand  |New Learning Composite maths |myhelper

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Question 5

Simplify:

(x+2) (x²–6x+8)–(2x–3)(2x²–x–1)

Sol :

=[x(x²–6x+8)+2(x²–6x+8)]-[2x(2x²–x–1)-3(2x²–x–1)]

=(x³–6x²+8x+2x²-12x+16)-[(4x³–2x²–2x-6x²+3x+3)]

=(x³–6x²+8x+2x²–12x+16)-4x³+2x²+2x+6x²–3x-3

=x³–6x²+8x+2x²–12x+16-4x³+2x²+2x+6x²–3x-3

=-3x³+4x²-5x+13