Question

Use suitable identities to find the following products : (I) (X+8) (X - 10) (II) (X+4) (X+10) class 8 Question
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Answer 1

Step-by-step explanation:

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Q:-Use suitable identities to find the following products : (I) (X+8) (X - 10) (II) (X+4) (X+10)

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solving (I)

$⟹(x + 8)(x - 10)$

Here this identify is used:-

$⟹(x + a)(x - b) = {x}^{2} + (a + b)x + ab$

$⟹(x + 8)(x - 10) = {x}^{2} + (8 + ( - 10))x + - 8 \times 10$

$⟹ {x}^{2} - 2x - 80 = 0$

solving (ii)

$⟹(x + 4)(x + 10)$

$⟹(x + 4) (x - 10) = {x}^{2} + (4 + ( - 10))x + 4 \times - 10$

$⟹ {x}^{2} - 6x - 40 = 0$

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HOPE IT HELPS YOU..

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Thankyou:)

Answer 2

Answer:

Identity:      

An identity is an equality which is true for

all values of a variable in the equality.

(x + a) (x +

b) = x²+(a + b) x +

ab

In an identity the right hand side expression

is called expanded form of the left hand side expression.

 

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Solution:

 

 

(i) Using identity,

[(x + a) (x +

b) = x² + (a + b) x +

ab]

In (x + 4) (x + 10),

 a = 4 &

b = 10

Now,

(x + 4) (x + 10)

= x² + (4 + 10)x + (4 × 10)

= x² + 14x+

40

(ii) (x + 8) (x –

10)

Using identity,

[(x + a) (x +

b) = x² + (a + b) x +

ab]

Here, a = 8 & b = –10

(x + 8) (x – 10)

= x²+{8+(– 10)}x +{8×(– 10)}

= x² + (8 – 10)x –

80

= x² – 2x –

80

 

(iii) (3x + 4) (3x –

5)

Using identity,

 [(x +

a) (x + b) = x² + (a + b) x +

ab]

Here, x = 3x , a = 4 &

b = -5

(3x + 4) (3x – 5)

=(3x)²+{4 + (-5)}3x +{4×(-5)}

= 9x² + 3x(4

– 5) – 20

= 9x² – 3x –

20

 

(iv) (y² +

3/2) (y² – 3/2)

Using identity,

[ (x + y)

(x –y) = x² – y²

]

Here, x = y² and y =

3/2

(y² + 3/2) (y² –

3/2)

= (y²)² –

(3/2)2

= y4– 9/4

 

(v) (3 – 2x) (3 + 2x)

Using identity,

[(x + y)

(x –y) = x² – y²

Here, x = 3 & y = 2x

(3 – 2x) (3 + 2x)

= 3² – (2x)²

=9– 4x²

 

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Hope this will help you...