Question

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

Answer 1

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) ⇒
`(2p+9)^2`

3. Factor
`81a^36-64b^16`

As
`a^2-b^2=(a+b)(a-b)`

∴
`81a^36-64b^16=(9a^18)^2-(8b^8)^2`

=
`(9a^18-8b^8)(9a^18+8b^8)` (Option B)

4. The differences between two squares is such that;

a²-b² = (a+b)(a-b)

`x^2-169=x^2-13^2=(a-13)(a+13)`, and

`t^2-4=t^2-2^2=(t-2)(t+2)`

First and third option correct.

Answer 2

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)