Factor. 25j^2 + 30j + 9 ______

Determine Perfect Square Trinomial: Determine if the quadratic expression can be factored as a perfect square trinomial. A perfect square trinomial is in the form (a + b)^2 = a^2 + 2ab + b^2. Here, we have 25j^2 + 30j + 9. We can see that 25j^2 is a perfect square, as (5j)^2 = 25j^2. Also, 9 is a perfect square, as 3^2 = 9. The middle term, 30j, is twice the product of 5j and 3, since 2 * 5j * 3 = 30j. This suggests that the expression might be a perfect square trinomial.Factor as Perfect Square: Factor the expression as a perfect square trinomial. If the expression is a perfect square trinomial, it can be factored as (a + b)^2. From Step 1, we have a = 5j and b = 3. So, the factored form should be (5j + 3)^2. Let's check if this is correct by expanding (5j + 3)^2: (5j + 3)(5j + 3) = 25j^2 + 15j + 15j + 9 = 25j^2 + 30j + 9. This matches the original expression, so the factorization is correct.

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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25j^2 + 30j + 9

Determine Perfect Square Trinomial: Determine if the quadratic expression can be factored as a perfect square trinomial. $\newline$ A perfect square trinomial is in the form $(a + b)^2 = a^2 + 2ab + b^2$ . $\newline$ Here, we have $25j^2 + 30j + 9$ . $\newline$ We can see that $25j^2$ is a perfect square, as $(5j)^2 = 25j^2$ . $\newline$ Also, $9$ is a perfect square, as $3^2 = 9$ . $\newline$ The middle term, $30j$ , is twice the product of $5j$ and $3$ , since $2 \times 5j \times 3 = 30j$ . $\newline$ This suggests that the expression might be a perfect square trinomial.
Factor as Perfect Square: Factor the expression as a perfect square trinomial. $\newline$ If the expression is a perfect square trinomial, it can be factored as $(a + b)^2$ . $\newline$ From Step $1$ , we have $a = 5j$ and $b = 3$ . $\newline$ So, the factored form should be $(5j + 3)^2$ . $\newline$ Let's check if this is correct by expanding $(5j + 3)^2$ : $\newline$ $(5j + 3)(5j + 3) = 25j^2 + 15j + 15j + 9 = 25j^2 + 30j + 9$ . $\newline$ This matches the original expression, so the factorization is correct.