Final answer:
To factor the expression x² + 3x²y +9y², we can use the pattern of perfect square trinomials. In this case, we can factor the expression as (x + 3y)².
Step-by-step explanation:
To factor the expression x² + 3x²y +9y², we can use the pattern of perfect square trinomials. A perfect square trinomial is in the form of (ax + b)². To apply this pattern, we need to identify the perfect square terms in the given expression. In this case, x² and 9y² are perfect squares.
We can rewrite the given expression as x² + 2(xy) + (3y)². Now, we can see that the expression matches the pattern (a + b)², where a = x and b = 3y. Thus, we can factor the expression as (x + 3y)².
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