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2x^(2)+26 x+84
If
2(x+a)(x+b) is equivalent to the given expression, what is the value of
ab ?

$2 x^{2}+26 x+84$ $\newline$ If $2(x+a)(x+b)$ is equivalent to the given expression, what is the value of $a b$ ?

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Solve equations using cube roots

Full solution

Q.

2 x^{2}+26 x+84

\newline

If

2(x+a)(x+b)

is equivalent to the given expression, what is the value of

a b

?

Expand expression: Expand the expression $2(x+a)(x+b)$ to find its equivalent quadratic form. $\newline$ Using the distributive property (FOIL method) to expand: $\newline$ $2(x+a)(x+b) = 2(x \times x + x \times b + a \times x + a \times b)(\newline$ = 2(x^2 + (b+a)x + ab)\)
Compare expanded form: Compare the expanded form with the given quadratic expression. $\newline$ We have $2x^2 + 26x + 84$ and $2(x^2 + (b+a)x + ab)$ . $\newline$ By comparing coefficients, we get: $\newline$ For $x^2$ term: $2 = 2$ (coefficients match, no need for further calculation) $\newline$ For $x$ term: $26 = 2(b+a)$ $\newline$ For constant term: $84 = 2ab$
Solve for $b+a$ : Solve for $b+a$ from the $x$ term. $\newline$ $26 = 2(b+a)$ $\newline$ Divide both sides by $2$ to isolate $(b+a)$ : $\newline$ $(b+a) = \frac{26}{2}$ $\newline$ $(b+a) = 13$
Solve for $ab$ : Solve for $ab$ from the constant term. $\newline$ $84$ = $2$ ab $\newline$ Divide both sides by $2$ to isolate $ab$ : $\newline$ $ab = \frac{$ $84$ }{ $2$ } $\newline$ $ab =$ $42$

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