Answer:
( 3a + b ) ( 2a − b )
Explanation:
For a polynomial of the form ax^2 + bx + c, rewrite the middle term as a sum of two terms whose product is a • c = 6 • − 1 = − 6 and whose sum is b = − 1.
1) Reorder terms. = 6a^2 − b^2 − ab
2) Reorder −b^2 and − ab. = 6a^2 − ab − b^2
3) Factor −1 out of −ab. = 6a^2 − ( ab ) − b^2
4) Rewrite −1 as 2 plus −3. = 6a^2 + ( 2 − 3 ) ( ab ) − b^2
5) Apply the distributive property. = 6a^2 + 2 ( ab ) − 3 ( ab ) − b^2
6) Remove unnecessary parentheses. = 6a^2 + 2ab − 3 ( ab ) − b^2
7) Remove unnecessary parentheses. = 6a^2 + 2ab − 3ab − b^2
Factor out the greatest common factor from each group.
1) Group the first two terms and the last two terms.
= ( 6a^2 + 2ab ) − 3ab − b^2
2) Factor out the greatest common factor (GCF) from each group.
= 2a ( 3a + b ) − b ( 3a + b )
3) Factor the polynomial by factoring out the greatest common factor,
3a + b .
= ( 3a + b ) ( 2a − b )