Question

please explain me how they have done first two sums.


SEE PIC ABOVE.click on it


explain me clearly only brainly moderaters . i want best answer.

❌❌NO SPAM♨️♨️❌

I am giving 20 pts.its urgent .my test is at 10a.m

I don't want solution i want its explanation​

Answer 1

Well, this is also a simple factorisation method. Just there are some common errors known as taking common, arranging orders,middle term splitting.

Now going to your solution :

Given equation :

⇒ 1/35 + (12/35)a + a²

At first taking 1/35 common, we get :

⇒ 1/35[1 + 12a + 35a²]

You must be wondering how (12a & 35a²) came, let me explain.

When we take 1/35 common, from the side 12a/35 we get :

→ 12a/35 = 1/35 × (12a)

Taking common from (12a/35) we get :

→ 12a

Now second part we can write a² like this :

→ a² = 1/35 × 35a²

Here, 35 will get cancelled and we will get back, a².

So taking 1/35 common from a² we get :

→ 35a²

Now going back to our solution :

Arranging the orders inside brackets,

⇒ 1/35[35a² + 12a + 1]

Now middle term splitting :

⇒ 1/35[35a² + 5a + 7a + 1]

⇒ 1/35[5a(7a + 1) + 1(7a + 1)]

⇒ 1/35[(5a + 1)(7a + 1)]

⇒ (1/35) (5a + 1)(7a + 1)

Hence,like this we get our required solution of the equation.

Answer 2

Let me make you understand the solution in a step by step manner :

1st step :

Since the terms are in fraction , we need to take $\dfrac{1}{35}$ common such that we can remove the fractions :

$= \dfrac{1}{35} + \dfrac{12}{35} a + {a}^{2} \\ = \dfrac{1}{35} \bigg \{1 + 12a + 35 {a}^{2} \bigg \}$

2nd step:

We are rearranging the terms according to our convenience ;

$= \dfrac{1}{35} \bigg \{35 {a}^{2} + 12a + 1 \bigg \}$

3rd step:

Now we are performing MID - TERM FACTORISATION ; We try to express 12a into 2 factors such that their products is 35a² ;

$= \dfrac{1}{35} \bigg \{35 {a}^{2} + (5a + 7a) + 1 \bigg \}$

4th step:

Taking common figures from the 2 factors :

$= \dfrac{1}{35} \bigg \{5a(7a +1 ) + 1(7a + 1 )\bigg \}$

5th step:

Now taking (7a + 1 ) as common ;

$= \dfrac{1}{35} \bigg \{(5a + 1)(7a + 1 )\bigg \}$