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Factorise 6a²-ab-b² completely


User TheEdge
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1 Answer

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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 )

User Qqilihq
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