Question

Qn04: Use suitable identities to find the following products:
(a) (x + 4) (x + 10)
(b) (x-8) (x - 10)​

Answer 1

Step-by-step explanation:

Given:-

(a) (x + 4) (x + 10)

(b) (x-8) (x - 10)

To find:-

Use suitable identities to find the following products:

(a) (x + 4) (x + 10)

(b) (x-8) (x - 10)

Solution:-

a) Given that (x + 4) (x + 10)

It is in the form of (x + a) (x + b )

Where a = 4 and b = 10

We know that

(x + a) (x + b ) = x^2+(a+b)x + ab

Now ,

(x + 4) (x + 10)

=> x^2+(4+10)x+(4×10)

=> x^2 + 14x + 40

(x + 4) (x + 10) = x^2 + 14x + 40

b)Given that (x - 8) (x -10)

It can be written as

[ x + (-8)] [ x + (-10)]

It is in the form of (x + a) (x + b )

Where a = -8 and b = -10

We know that

(x + a) (x + b ) = x^2+(a+b)x + ab

Now ,

(x -8) (x - 10)

=> x^2 + (-8 - 10) x + (-8 × -10)

=> x^2 +(- 18) x + 80

=> x^2 -18 x + 80

(x - 8) (x - 10) = x^2 - 18x + 80

Answer:-

a)(x + 4) (x + 10) = x^2 + 14x + 40

b)(x - 8) (x - 10) = x^2 - 18x + 80

Used Identity:-

• (x + a) (x + b ) = x^2+(a+b)x + ab

Answer 2

$(x + 4)(x + 10) \\ By \: using \: the \: identity(x \times + a)(x + b) = {x}^{2} + (a + b)x + ab \\(x + 4)(x + 10) = {x}^{2} + (4 + 10)x + 4 \times 10 \\ = {x}^{2} + 14x + 40$

$(x + 8)(x - 10) \\ By \: using \: the \: identity \: (x + a)(x + b) = {x}^{2} + (a + b)x + ab \\ (x + 8)(x - 10) = {x}^{2} + (8 - 10)x + (8)( - 10) \\ = {x}^{2} - 2x - 80$