Question

factorize 5(3x+y)^2+6(3x+y)-8

Answer 1

Answer :

Now, 5 (3x + y)² + 6 (3x + y) - 8

= 5 (3x + y)² + 10 (3x + y) - 4 (3x + y) - 8

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

= (3x + y + 2) (15x + 5y - 4),

which is the required factorization.

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Answer 2

Given,

5(3x+y)²+6(3x+y)-8

To find,

The factors of the given expression.

Solution,

The factors of 5(3x+y)²+6(3x+y)-8 will be (3x+y+2) (15x+5y-4).

We can easily solve this problem by following the given steps.

Now, to factories the given expression, we will have to split its middle term, 6(3x+y), such that their subtraction will give the middle term and their multiplication will give 5(3x+y)² × (-8) or -40(3x+y)².

So, these two terms are 10(3x+y) and -4(3x+y).

5(3x+y)²+6(3x+y)-8

5(3x+y)²+10(3x+y)-4(3x+y)-8

Taking 5(3x+y) common from the first two terms and -4 from the last two terms,

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

Taking (3x+y+2) common,

(3x+y+2) [ 5(3x+y)-4]

(3x+y+2) (15x+5y-4)

Hence, the factors of 5(3x+y)²+6(3x+y)-8 are (3x+y+2) (15x+5y-4).