Question

factorise
10ab+5a+5b+2​

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

((5 • (a2)) - 10ab) + 5b2

STEP

2

:

Equation at the end of step

2

:

(5a2 - 10ab) + 5b2

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

5a2 - 10ab + 5b2 = 5 • (a2 - 2ab + b2)

Trying to factor a multi variable polynomial :

4.2 Factoring a2 - 2ab + b2

Try to factor this multi-variable trinomial using trial and error

Found a factorization : (a - b)•(a - b)

Detecting a perfect square :

4.3 a2 -2ab +b2 is a perfect square

It factors into (a-b)•(a-b)

which is another way of writing (a-b)2

How to recognize a perfect square trinomial:

• It has three terms

• Two of its terms are perfect squares themselves

• The remaining term is twice the product of the square roots of the other two terms

Final result :

5 • (a - b)2