Question

use the suitable identities to find the following product iii) (3x+4)(3x-5)​

Answer 1

Step-by-step explanation:

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

 

Answer 2

Step-by-step explanation:

We have to use identity 4 (x+a)(x+b)=x2+(a+b)x+ab

(3x+4)(3x-5)

=(3x+4){3x+(-5)}

here x=3x a=4 and b=-5

=3x2+{4+(-5)}+4×(-5)

=9x2-1-20