Question

Factorise : 7a^2 +48ab - 7b^2​

Answer 1

Answer:

7a2+14ab+7b2  

Final result :

 7 • (a + b)2

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "b2"   was replaced by   "b^2".  1 more similar replacement(s).

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((7 • (a2)) +  14ab) +  7b2

Step  2  :

Equation at the end of step  2  :

 (7a2 +  14ab) +  7b2

Step  3  :

Step  4  :

Pulling out like terms :

4.1     Pull out like factors :

  7a2 + 14ab + 7b2  =   7 • (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 :

 7 • (a + b)2

Processing ends successfully

Step-by-step explanation:

Answer 2

Step-by-step explanation:

7a^2+49ab-1ab-7b^2

7a^2+49ab-1ab-7b^27a(a+7b)-b(a+7b)

7a^2+49ab-1ab-7b^27a(a+7b)-b(a+7b)(7a-b) (a-7b)