S.chand books class 8 maths solution chapter 14 Factorisation exercise 14 D

EXERCISE 14 D

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Q1 | Ex-14D | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 1

x² + 4x + 4

Sol :

$=x^{2}+4 x+4$

$=x^{2}+2 \times x \times 2+(2)^{2}$ $\left[a^{2}+2 a b+b^{2}=(a+b)^{2}\right]$

$=(x-2)^{2}$

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Q2 | Ex-14D | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 2

x² + 6x + 9

Sol :

$=x^{2}+2\times x\times 3+3^{2}$ $\left[a^{2}+2a b+b^{2}=(a+b)^2\right]$

$=(x+3)^{2}$

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Q3 | Ex-14D | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 3

x² - 10x + 25

Sol :

$=x^{2}-2 \times x \times 5+5^{2}$ $\left[a^{2}+2 a b+b^{2}=(a+b)^{2}\right]$

$=(x-5)^{2}$

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Q4 | Ex-14D | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 4

4x² - 4x + 1

Sol :

$=(2 x)^{2}-2 \times 2x \times 1+1^{2}$  $\left[a^{2}+2 a b+b^{2}=(a-b)^2\right]$

$=(2 x-1)^{2}$

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Q5 | Ex-14D | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 5

a² + 10ab + 25b²

Sol :

$=a^{2}+2 \times 5 b \times a+(5 b)^{2}$ $\left[a^{2}+2 a b+b^{2}=(a+b)^{2}\right]$

$=\left(a^{2}+5 b\right)^{2}$

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Q6 | Ex-14D | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 6

x² - 8xy + 16y²

Sol :

$=x^{2}-2 x \times 4 y+(4 y)^{2}$ $\left[a^{2}-2 a b+b^{2}=(a-b)^{2}\right]$

$=\left(x-4 y\right)^{2}$

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Q7 | Ex-14D | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 7

4x² + 20xy + 25y²

Sol :

$=(2 x)^{2}+2 \times 2x \times 5 y+(5 y)^{2}$ $\left[a^{2}+2 a b+b^{2}=(a+b)^{2}\right]$

$=(2x+5 y)^{2}$

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Q8 | Ex-14D | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 8

64x² - 80xy + 25y²

Sol :

$=(8x)^{2}-2 \times 8 x \times 5 y+(5 y)^{2}$ $\left[a^{2}-2 a b+b^{2}=(a-b)^{2}\right.$

$=(8x-5 y)^{2}$

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Q9 | Ex-14D | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 9

x⁴ + 6x² + 9

Sol :

$\left(x^{2}\right)^{2}+2 \times x^{2} \times 3+(3)^{2}$ $\left[a^{2}+2 a b+b^{2}=(a+b)^{2}\right]$

$=\left(x^{2}+3\right)^{2}$

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Q10 | Ex-14D | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 10

4x⁴ - 12x² + 9

Sol :

$=\left(2 x^{2}\right)^{2}-2 \times 2 x^{2} \times 3+(3)^{2}$ $\left[a^{2}-2 a b+b^{2}=(a-b)^{2}\right]$

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

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Q11 | Ex-14D | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 11

a² - 2 +$\dfrac{1}{a^2}$

Sol :

$=(a)^{2}-2 \times a \times \frac{1}{a}+\left(\frac{1}{a}\right)^{2}$ $\left[a^{2}-2 a b+b^{2}=(a+b)^{2}\right]$

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

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Q12 | Ex-14D | Class 8 | S.Chand | Composite maths | chapter 14 |Factorisation | myhelper

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Question 12

x² + x + $\dfrac{1}{4}$

Sol :

$=x^{2}+x+\frac{1}{4}$

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

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