Rewrite the expression as a product of four linear factors: (12x^(2)+13 x)^(2)+4(12x^(2)+13 x)+3 Answer:

Recognize Perfect Square Trinomial: Recognize the given expression as a perfect square trinomial. The expression given is (12x^2 + 13x)^2 + 4(12x^2 + 13x) + 3. This resembles the form of a perfect square trinomial a^2 + 2ab + b^2, which factors into (a + b)^2.Factor as Perfect Square: Factor the expression as a perfect square trinomial. Let's set a = (12x^2 + 13x) and b = 2, then the expression becomes a^2 + 2ab + b^2, which is a perfect square trinomial. So, the expression can be written as ((12x^2 + 13x) + 2)^2.Expand for Verification: Expand the perfect square trinomial to verify the factorization. Expanding ((12x^2 + 13x) + 2)^2 gives us (12x^2 + 13x)^2 + 2*(12x^2 + 13x)*2 + 2^2, which simplifies to (12x^2 + 13x)^2 + 4(12x^2 + 13x) + 4. However, we notice that the original expression has a constant term of 3, not 4. This means we made a mistake in our factorization.

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Rewrite the expression as a product of four linear factors:

(12x^(2)+13 x)^(2)+4(12x^(2)+13 x)+3
Answer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(12 x^{2}+13 x\right)^{2}+4\left(12 x^{2}+13 x\right)+3$ $\newline$ Answer:

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Q. Rewrite the expression as a product of four linear factors:

\newline

\left(12 x^{2}+13 x\right)^{2}+4\left(12 x^{2}+13 x\right)+3

\newline

Answer:

Recognize Perfect Square Trinomial: Recognize the given expression as a perfect square trinomial. The expression given is $(12x^2 + 13x)^2 + 4(12x^2 + 13x) + 3$ . This resembles the form of a perfect square trinomial $a^2 + 2ab + b^2$ , which factors into $(a + b)^2$ .
Factor as Perfect Square: Factor the expression as a perfect square trinomial. $\newline$ Let's set $a = (12x^2 + 13x)$ and $b = 2$ , then the expression becomes $a^2 + 2ab + b^2$ , which is a perfect square trinomial. $\newline$ So, the expression can be written as $((12x^2 + 13x) + 2)^2$ .
Expand for Verification: Expand the perfect square trinomial to verify the factorization. $\newline$ Expanding $((12x^2 + 13x) + 2)^2$ gives us $(12x^2 + 13x)^2 + 2*(12x^2 + 13x)*2 + 2^2$ , which simplifies to $(12x^2 + 13x)^2 + 4(12x^2 + 13x) + 4$ . $\newline$ However, we notice that the original expression has a constant term of $3$ , not $4$ . This means we made a mistake in our factorization.