Question

let's factorise 7ax²+14ax+7a​

Answer 1

Step by Step Solution

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Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

STEP

1

:

Equation at the end of step 1

(7ax2 + 14ax) + 7a

STEP

2

:

STEP

3

:

Pulling out like term Pull out like factors :

7ax2 + 14ax + 7a = 7a • (x2 + 2x + 1)

Trying to factor by splitting the middle term

3.2 Factoring x2 + 2x + 1

The first term is, x2 its coefficient is 1 .

The middle term is, +2x its coefficient is 2 .

The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 1 • 1 = 1

Step-2 : Find two factors of 1 whose sum equals the coefficient of the middle term, which is 2 .

-1 + -1 = -2

1 + 1 = 2 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 1 and 1

x2 + 1x + 1x + 1

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x+1)

Add up the last 2 terms, pulling out common factors :

1 • (x+1)

Step-5 : Add up the four terms of step 4 :

(x+1) • (x+1)

Which is the desired factorization

Multiplying Exponential Expressions:

3.3 Multiply (x+1) by (x+1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (x+1) and the exponents are :

1 , as (x+1) is the same number as (x+1)1

and 1 , as (x+1) is the same number as (x+1)1

The product is therefore, (x+1)(1+1) = (x+1)2

Final result :

7a • (x + 1)2

I hope it's help you:))))))))