Factor. 9t^2 + 12t + 4 ______

Check Factoring Possibility: Determine if the quadratic expression can be factored using the form (at + b)^2 = a^2t^2 + 2abt + b^2. The given expression is 9t^2 + 12t + 4. We need to check if there are numbers a and b such that (at + b)^2 matches the given expression.Identify Square Roots: Identify the square root of the first term and the last term. The square root of 9t^2 is 3t, and the square root of 4 is 2. So, we will check if (3t + 2)^2 equals the given expression.Expand and Verify: Expand (3t + 2)^2 to verify if it equals the given expression. (3t + 2)^2 = (3t + 2)(3t + 2) = 9t^2 + 6t + 6t + 4 = 9t^2 + 12t + 4 This matches the given expression exactly.Write Factored Form: Write the factored form of the expression. Since (3t + 2)^2 equals the given expression, the factored form is (3t + 2)(3t + 2) or (3t + 2)^2.

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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9t^2 + 12t + 4

Check Factoring Possibility: Determine if the quadratic expression can be factored using the form $(at + b)^2 = a^2t^2 + 2abt + b^2$ . The given expression is $9t^2 + 12t + 4$ . We need to check if there are numbers $a$ and $b$ such that $(at + b)^2$ matches the given expression.
Identify Square Roots: Identify the square root of the first term and the last term. $\newline$ The square root of $9t^2$ is $3t$ , and the square root of $4$ is $2$ . So, we will check if $(3t + 2)^2$ equals the given expression.
Expand and Verify: Expand $(3t + 2)^2$ to verify if it equals the given expression. $(3t + 2)^2 = (3t + 2)(3t + 2) = 9t^2 + 6t + 6t + 4 = 9t^2 + 12t + 4$ This matches the given expression exactly.
Write Factored Form: Write the factored form of the expression. $\newline$ Since $(3t + 2)^2$ equals the given expression, the factored form is $(3t + 2)(3t + 2)$ or $(3t + 2)^2$ .