Question

Expand

3(x+4)


expand and simplify

4(x+5)-2(x-3)


expand

(x+2)(x+7


Factorize fully

12x-18

Answer 1

The working of expressions is shown below.

Explanation:

We are given the following information:

a) Expand

`3(x+4)\\3* x + 3* 4\\3x + 12`

b) Expand and simplify

`4(x+5)-2(x-3)\\=(4x + 20) -(2x-6)\\=( 4x-2x) + (20 + 6)\\= 2x + 26\\=2(x +13)`

c) Expand

`(x+2)(x+7)\\=x* x + x* 7 + 2* x + 2* 7\\= x^2 + 7x + 2x + 14\\=x^2 + 9x +14`

d) Factorize fully

`12x-18\\=6(2x-3)`

Answer 2

1)
`3(x+4)=3x+12`

2)
`4(x+5)-2(x-3)=2x+26`

3)
`(x+2)(x+7)=x^2+9x+14`

4)
`12x-18=6(2x-3)`

Explanation:

1) Expression :
`3(x+4)`

To find : Expand the expression ?

Solution :

`3(x+4)`

Applying distributive property,
`a(b+c)=ab+ac`

`3(x+4)=3x+12`

2) Expression :
`4(x+5)-2(x-3)`

To find : Expand and simplify the expression ?

Solution :

`4(x+5)-2(x-3)`

Applying distributive property,
`a(b+c)=ab+ac`

`4(x+5)-2(x-3)=4x+20-2x+6`

`4(x+5)-2(x-3)=2x+26`

3) Expression :
`(x+2)(x+7)`

To find : Expand the expression ?

Solution :

`(x+2)(x+7)`

Applying distributive property,
`a(b+c)=ab+ac`

`(x+2)(x+7)=x(x+7)+2(x+7)`

`(x+2)(x+7)=x^2+7x+2x+14`

`(x+2)(x+7)=x^2+9x+14`

4) Expression :
`12x-18`

To find : Factorize the expression ?

Solution :

`12x-18`

Taking the common term,

`12x-18=6(2x-3)`