Which trinomials are perfect square trinomials?

choose exactly two answers that are correct.

a2 + 4a + 16

a2 + 14a + 49

a2 + 15a + 75

a2 + 26a + 169

You can know a perfect square trinomial:

i) if the coefficient of a² = 1.

ii) If you divide the middle number coefficient by 2 and you square it you get the last term.

Take for example the first option: 

For all the options, the coefficient of a² = 1

a² + 4a + 16.

Coefficient of a = 4.
4/2 = 2
2² = 4, this does not equal the last term so it is not a perfect square trinomial.

a² + 14a + 49.

Coefficient of a = 14.
14/2 = 7
7² = 49, this is equal the last term so it is a perfect square trinomial.
And the perfect square is (a +7)²

Similarly if you test the last option.

a² + 26a + 169.

Coefficient of a = 26.
26/2 = 13
13² = 169, this is equal the last term so it is a perfect square trinomial.
And the perfect square is (a +13)²

So the only two options are: a² + 14a + 49 and a² + 26a + 169.

Other options do not pass this test.

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