Factor as the product of two binomials. 81+18 x+x^(2)=

Recognize the structure: Recognize the structure of the expression. The given expression is a quadratic in the form of x^2 + bx + c. We need to find two numbers that multiply to give ac (where a is the coefficient of x^2 and c is the constant term) and add to give b (the coefficient of x).Identify the coefficients: Identify the coefficients a, b, and c in the expression 81 + 18x + x^2. Here, a = 1 (coefficient of x^2), b = 18 (coefficient of x), and c = 81 (constant term).Find two numbers: Find two numbers that multiply to ac (1*81 = 81) and add up to b (18). The numbers that satisfy these conditions are 9 and 9, since 9 * 9 = 81 and 9 + 9 = 18.Write the expression: Write the expression as the product of two binomials using the numbers found in Step 3. The factored form is (x + 9)(x + 9) or (x + 9)^2.

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Algebra 1

Factor quadratics: special cases

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Q. Factor as the product of two binomials.

\newline

81+18x+x^{2}=

Recognize the structure: Recognize the structure of the expression. $\newline$ The given expression is a quadratic in the form of $x^2 + bx + c$ . We need to find two numbers that multiply to give $ac$ (where $a$ is the coefficient of $x^2$ and $c$ is the constant term) and add to give $b$ (the coefficient of $x$ ).
Identify the coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the expression $81 + 18x + x^2$ . $\newline$ Here, $a = 1$ (coefficient of $x^2$ ), $b = 18$ (coefficient of $x$ ), and $c = 81$ (constant term).
Find two numbers: Find two numbers that multiply to $ac$ ( $1 \times 81 = 81$ ) and add up to $b$ ( $18$ ). $\newline$ The numbers that satisfy these conditions are $9$ and $9$ , since $9 \times 9 = 81$ and $9 + 9 = 18$ .
Write the expression: Write the expression as the product of two binomials using the numbers found in Step $3$ . $\newline$ The factored form is $(x + 9)(x + 9)$ or $(x + 9)^2$ .