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timurjin [86]
2 years ago
11

Factorize x^2/16+xy+4y^2​

Mathematics
1 answer:
lisov135 [29]2 years ago
4 0

Answer:

\frac{x^2}{16} +xy+4y^2 can be factored out as: (\frac{x}{4} +2\,y)^2

Step-by-step explanation:

Recall the formula for the perfect square of a binomial :

(a+b)^2=a^2+2ab+b^2

Now, let's try to identify the values of a and b in the given trinomial.

Notice that the first term and the last term are perfect squares:

\frac{x^2}{16} = (\frac{x}{4} )^2\\4y^2=(2y)^2

so, we can investigate what the middle term would be considering our a=\frac{x}{4}, and b=2y:

2\,a\,b=2\,(\frac{x}{4}) \,(2\,y)=x\,y

Therefore, the calculated middle term agrees with the given middle term, so we can conclude that this trinomial is the perfect square of the binomial:

(\frac{x}{4} +2\,y)^2

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