Question

Factorize the following perfect squares.
(a) x^{2} – 12x + 36
(b) 64a^{2} - 48ab + 9b^{2}
(c) 16x^{2} + 40xy + 25y^{2}
(d) a^{2} - 22ab + 121b^{2}

Answer 1

Answer:

Step-by-step explanation:

(B) STEP

1

:

Equation at the end of step 1

 ((64 • (a2)) -  48ab) +  32b2

STEP  

2

:

Equation at the end of step

2

:

 (26a2 -  48ab) +  32b2

STEP

3

:

Trying to factor a multi variable polynomial

3.1    Factoring    64a2 - 48ab + 9b2  

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

Found a factorization  :  (8a - 3b)•(8a - 3b)

Detecting a perfect square :

3.2    64a2  -48ab  +9b2  is a perfect square  

It factors into  (8a-3b)•(8a-3b)

which is another way of writing  (8a-3b)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 :

 (8a - 3b)2

(D)   STEP 1

:

Equation at the end of step 1

 ((a2) +  22ab) +  112b2

STEP

2

:

Trying to factor a multi variable polynomial

2.1    Factoring    a2 + 22ab + 121b2  

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

Found a factorization  :  (a + 11b)•(a + 11b)

Detecting a perfect square :

2.2    a2  +22ab  +121b2  is a perfect square  

It factors into  (a+11b)•(a+11b)

which is another way of writing  (a+11b)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 :

 (a + 11b)2