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Norma-Jean [14]
3 years ago
7

7. All of the following are perfect square trinomials EXCEPT one. Which is it?

Mathematics
1 answer:
wolverine [178]3 years ago
8 0

Answer:

All answers EXCEPT answer C. are perfect square trinomials.

Step-by-step explanation:

A perfect square trinomial is polynomial that satisfies the following condition:

(a+b)^{2} = a^{2}+2\cdot a \cdot b + b^{2}, \forall\,a,b\in\mathbb{R}

Let prove if each option observe this:

a) 4\cdot x^{2} + 12\cdot x\cdot y + 9\cdot y^{2}

1) 4\cdot x^{2} + 12\cdot x\cdot y + 9\cdot y^{2} Given

2) (2\cdot x)^{2}+ 2\cdot (2\cdot x)\cdot (3\cdot y)+(3\cdot y)^{2} Definition of power/Distributive, associative and commutative properties.

3) a = 2\cdot x, b = 3\cdot y Definition of perfect square trinomial/Result.

b) 9\cdot a^{2}-36\cdot a + 36

1) 9\cdot a^{2}-36\cdot a + 36 Given.

2) (3\cdot a)^{2}-2\cdot (3\cdot a)\cdot 6 + 6^{2} Definition of power/Distributive, associative and commutative properties.

3) a = 3\cdot a, b = 6 Definition of perfect square trinomial/Result.

c) x\cdot y^{2}-4\cdot x^{2}\cdot y^{2}+4\cdot x^{2}\cdot y^{2}

1) x\cdot y^{2}-4\cdot x^{2}\cdot y^{2}+4\cdot x^{2}\cdot y^{2} Given

2) x\cdot y\cdot (1-4\cdot x+4\cdot x) Distributive property.

3) x\cdot y \cdot 1 Existence of the additive inverse/Modulative property.

4) x\cdot y Modulative property/Result.

d) a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4}

1) a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4} Given

2) (a\cdot b)^{2}+2\cdot (a\cdot b)\cdot (2\cdot a^{2})+(2\cdot a^{2}) Definition of power/Distributive, associative and commutative properties.

3) a = a\cdot b, b = 2\cdot a^{2} Definition of perfect square trinomial.

All answers EXCEPT answer C. are perfect square trinomials.

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