Factor completely. 4x^(2)+36 xy+81y^(2)=

Identify Quadratic Trinomial Form: Identify the form of the quadratic trinomial. The given expression 4x^2 + 36xy + 81y^2 represents the form a^2 + 2ab + b^2.Rewrite 4x^2 as a^2: Rewrite 4x^2 in the form of a^2. 2^2 = 4 4x^2 = (2x)^2Rewrite 81y^2 as b^2: Rewrite 81y^2 in the form of b^2. 9^2 = 81 81y^2 = (9y)^2Identify Values of a and b: Identify the values of a and b. Compare (2x)^2 with a^2 and (9y)^2 with b^2. a = 2x b = 9yVerify Middle Term Matches 2ab: Verify that the middle term 36xy matches 2ab. 2 * (2x) * (9y) = 36xyWrite Factored Form of Expression: Write the factored form of the expression 4x^2 + 36xy + 81y^2. a^2 + 2ab + b^2 = (a + b)^2 4x^2 + 36xy + 81y^2 = (2x + 9y)^2 Factored form: (2x + 9y)^2

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Algebra 2

Factor quadratics

Full solution

Q. Factor completely.

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4 x^{2}+36 x y+81 y^{2}=

Identify Quadratic Trinomial Form: Identify the form of the quadratic trinomial. $\newline$ The given expression $4x^2 + 36xy + 81y^2$ represents the form $a^2 + 2ab + b^2$ .
Rewrite $4x^2$ as $a^2$ : Rewrite $4x^2$ in the form of $a^2$ . $\newline$ $2^2 = 4$ $\newline$ $4x^2 = (2x)^2$
Rewrite $81y^2$ as $b^2$ : Rewrite $81y^2$ in the form of $b^2$ . $\newline$ $9^2 = 81$ $\newline$ $81y^2 = (9y)^2$
Identify Values of a and b: Identify the values of $a$ and $b$ . $\newline$ Compare $(2x)^2$ with $a^2$ and $(9y)^2$ with $b^2$ . $\newline$ $a = 2x$ $\newline$ $b = 9y$
Verify Middle Term Matches $2ab$ : Verify that the middle term $36xy$ matches $2ab$ . $\newline$ $2 \times (2x) \times (9y) = 36xy$
Write Factored Form of Expression: Write the factored form of the expression $4x^2 + 36xy + 81y^2$ . $\newline$ $a^2 + 2ab + b^2 = (a + b)^2$ $\newline$ $4x^2 + 36xy + 81y^2 = (2x + 9y)^2$ $\newline$ Factored form: $(2x + 9y)^2$