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Which trinomials are perfect square trinomials?

Select each correct answer.




a2+26a+169

a2+4a+16

a2+14a+49

a2+15a+75


Factor completely.

4p² + 36p + 81

Express the answer in the form (ap+b)2 .


Enter your answer in the box.






Factor.

81a36−64b16




(9a6−8b4)(9a6+8b4)

(9a18−8b8)(9a18+8b8)

(9a6−8b4)2

(9a18−8b8)2




Which expressions are differences of squares?

Select each correct answer.




x2−169

h2−20

t2−4

a2+1

Respuesta :

1. the perfect squares in this case are
a²+26a+169 = (a+13)²
a²+14a+49 = (a+7)²

2. factorising 
4p²+36p+81
 product = 324
      sum = 36
numbers are 18 and 18
Thus , 4p²+18p+18p+81
          2p(2p+9) +9p(2p+9)
thus, (2p+9p)(2p+9p)

3. Factor 81a36-64b16
this is the difference between two squares, such that;
a²-b² = (a+b)(a-b)
therefore, 81a36 -64b16 will be;
(9a18-8b8)(9a18+8b8)

4.  The differences between two squares is such that;
a²-b² = (a+b)(a-b)
therefore in this case, the difference between two squares will be;
x²-169 = (a-13)(a+13), and
t²-4     = (t-4)(t+4)

Step-by-step explanation:

1. the perfect squares in this case are

a²+26a+169 = (a+13)²

a²+14a+49 = (a+7)²

First and fourth option are correct.

2. factorise  4p²+36p+81

Product = 324 and sum = 36

numbers are 18 and 18

∴  4p²+18p+18p+81

⇒ 2p(2p+9) +9(2p+9)

⇒ (2p+9)(2p+9) ⇒ [tex](2p+9)^2[/tex]

3. Factor [tex]81a^36-64b^16[/tex]

As [tex]a^2-b^2=(a+b)(a-b)[/tex]

∴  [tex]81a^36-64b^16=(9a^18)^2-(8b^8)^2[/tex]

                                   =[tex](9a^18-8b^8)(9a^18+8b^8)[/tex]  (Option B)

4.  The differences between two squares is such that;

a²-b² = (a+b)(a-b)

[tex]x^2-169=x^2-13^2=(a-13)(a+13)[/tex], and

[tex]t^2-4=t^2-2^2=(t-2)(t+2)[/tex]

First and third option correct.




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