S.chand publication New Learning Composite mathematics solution of class 8 Chapter 6 Factorisation of Algebraic Expressions Exercise 6D

 Exercise 6D

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State whether or not the expression is a trinomial square. If it is, factorise the expression.

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Q1 | Ex-6C | Class 8 | S.Chand | New Learning Composite maths | chapter 6 |Factorisation of Algebraic Expressions | myhelper

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Question 1

a² + 4ab + 4b²

Sol :

=a²+2.a.2b+(2b)²
=(a+2b)²

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Q2 | Ex-6C | Class 8 | S.Chand | New Learning Composite maths | chapter 6 |Factorisation of Algebraic Expressions | myhelper

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Question 2

4x² – 4x + 1

Sol :

=(2x)²-2.2x.1+(1)²

=(2x-1)²

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Q3 | Ex-6C | Class 8 | S.Chand | New Learning Composite maths | chapter 6 |Factorisation of Algebraic Expressions | myhelper

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Question 3

36p² – 60pq + 25q²

Sol :

=(6p)²-2.6p.5q+(5q)²

=(6p-5q)²

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Q4 | Ex-6C | Class 8 | S.Chand | New Learning Composite maths | chapter 6 |Factorisation of Algebraic Expressions | myhelper

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Question 4

x² – 2xy – y²

Sol :

=x²–2xy–y²

NO

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Q5 | Ex-6C | Class 8 | S.Chand | New Learning Composite maths | chapter 6 |Factorisation of Algebraic Expressions | myhelper

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Question 5

49y² – 14y + 1

Sol :

=(7y)²– 2.7y.1+1²

=(7y-1)²

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Q6 | Ex-6C | Class 8 | S.Chand | New Learning Composite maths | chapter 6 |Factorisation of Algebraic Expressions | myhelper

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Question 6

9x²y² + 6xyz + z²

Sol :

=(3xy)²+2.3xy.7+z²

=(3xy+z)²

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Q7 | Ex-6C | Class 8 | S.Chand | New Learning Composite maths | chapter 6 |Factorisation of Algebraic Expressions | myhelper

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Question 7

4m²+24m+9

Sol :

NO

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Q8 | Ex-6C | Class 8 | S.Chand | New Learning Composite maths | chapter 6 |Factorisation of Algebraic Expressions | myhelper

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Question 8

16b² – 60by + 25y²

Sol :

NO

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Q9 | Ex-6C | Class 8 | S.Chand | New Learning Composite maths | chapter 6 |Factorisation of Algebraic Expressions | myhelper

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Question 9

49x⁴ – 112x²y² + 64y⁴

Sol :

=(7x)²-2.7x.8y+(8y)²

=(7x²-8y²)²

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Q10 | Ex-6C | Class 8 | S.Chand | New Learning Composite maths | chapter 6 |Factorisation of Algebraic Expressions | myhelper

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Question 10

25x² + 20x + 1

Sol :

NO

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Q11 | Ex-6C | Class 8 | S.Chand | New Learning Composite maths | chapter 6 |Factorisation of Algebraic Expressions | myhelper

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Question 11

$\frac{x^2}{9y^2}-\frac{2}{15}+\frac{y^2}{25x^2}$

Sol :

$=\left(\frac{x}{3y}\right)^2-2.\frac{x}{3y}.\frac{y}{5x}+\left(\frac{y}{5x}\right)^2$

$=\left(\frac{x}{3y}-\frac{y}{5x}\right)^2$

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Q12 | Ex-6C | Class 8 | S.Chand | New Learning Composite maths | chapter 6 |Factorisation of Algebraic Expressions | myhelper

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Question 12

a²+a+ ¼

Sol :

$=a^2+2.a.\frac{1}{2}+\left(\frac{1}{2}\right)^2$

$=\left(a+\frac{1}{x}\right)^2$

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Q13 | Ex-6C | Class 8 | S.Chand | New Learning Composite maths | chapter 6 |Factorisation of Algebraic Expressions | myhelper

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Question 13

1+18pq+81p²q²

Sol :

=1²+2.9pq.1+(9pq)²

=(1+9pq)²

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Q14 | Ex-6C | Class 8 | S.Chand | New Learning Composite maths | chapter 6 |Factorisation of Algebraic Expressions | myhelper

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Question 14

4–20b+25b²

Sol :

=2²-2.4.5b+5b²

=(2+5b)²

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Q15 | Ex-6C | Class 8 | S.Chand | New Learning Composite maths | chapter 6 |Factorisation of Algebraic Expressions | myhelper

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Question 15

$\frac{4}{9}x^2+\frac{16}{15}xy+\frac{16}{25}y^2$

Sol :

$=\left(\frac{2}{3}x\right)^2+2.\frac{2x}{3}.\frac{4y}{5}+\left(\frac{4}{5}y\right)^2$

$=\left(\frac{2x}{3}+\frac{4y}{5}\right)^2$