Question

Factorize the following:5(3a + b)² +6 (3a +b) - 8​

Answer 1

Answer:

Step-by-step explanation:

Here, following formula will be used

(a+b)²= a²+b²+2ab

question

5(3a + b)² +6 (3a +b) - 8​

=> we will take out 3 as common number to make the term (3a+b) to fit formula requirement

=> 5x3 (a+b/3)²+6(3a+b)-8

=> 15(a²+b²/9+2xaxb/3)+18a+6b-8

here, we have expanded the formula

=> 15a²+15b²/9+15x2ab/3+18a+6b-8

=> 15a²+5b²/3+10ab+18a+6b-8

Answer 2

Answer:

[5(3a +b) - 4][ (3a +b) + 2]

Step-by-step explanation:

We can factorize the equation as follows:

5(3a + b)² +6 (3a +b) - 8​ ..(1)

Let (3a +b) be y, therefore the question becomes

5y^2 + 6y - 8. .... (2)

Next, we have to multiply the first and last term together, and then find the factor such that the factors will result to 6. This is illustrated below:

5y^2 x - 8 = -40y^2

Factors of -40y^2 = 10y and - 4y

Substituting 10y and - 4y into the into equation (2) in place of 6y, we obtain:

5y^2 + 6y - 8

5y^2 + 10y - 4y - 8

Now, we factorize as follows:

5y(y + 2) - 4(y + 2)

Since we have same entity in both brackets, we shall pick one:

(5y - 4)(y + 2). .....(3)

But recall

y = (3a +b)

Substituting the value of y into equation (3), we have:

(5y - 4)(y + 2).

[ 5(3a +b) - 4 ][ (3a +b) + 2 ]