What is (-(x^2)/8+ax+1)(-(x^2)/9+bx+1) ?

The solution to (-(x^2)/8+ax+1)(-(x^2)/9+bx+1) is ((-x^2+8ax+8)(-x^2+9bx+9))/(72)

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simplify (-(x^2)/8+ax+1)(-(x^2)/9+bx+1)

simplify

(- \frac{x ^{2}}{8} + a x + 1) (- \frac{x ^{2}}{9} + b x + 1)

\frac{( - x ^{2} + 8 a x + 8 ) ( - x ^{2} + 9 b x + 9 )}{72}

Solution steps

(- \frac{x ^{2}}{8} + a x + 1) (- \frac{x ^{2}}{9} + b x + 1)

Simplify

- \frac{x ^{2}}{8} + a x + 1 : \frac{- x ^{2} + 8 a x + 8}{8}

= \frac{- x ^{2} + 8 a x + 8}{8} (- \frac{x ^{2}}{9} + b x + 1)

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( - x ^{2} + 8 a x + 8 ) ( - \frac{x ^{2}}{9} + b x + 1 )}{8}

Simplify

(- x^{2} + 8 a x + 8) (- \frac{x ^{2}}{9} + b x + 1) : \frac{( - x ^{2} + 8 a x + 8 ) ( - x ^{2} + b x \cdot 9 + 9 )}{9}

= \frac{\frac{( - x ^{2} + 8 a x + 8 ) ( - x ^{2} + b x \cdot 9 + 9 )}{9}}{8}

Apply the fraction rule:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

= \frac{( - x ^{2} + 8 a x + 8 ) ( - x ^{2} + b x \cdot 9 + 9 )}{9 \cdot 8}

Multiply the numbers:

9 \cdot 8 = 72

= \frac{( - x ^{2} + 8 a x + 8 ) ( - x ^{2} + b x \cdot 9 + 9 )}{72}

= \frac{( - x ^{2} + 8 a x + 8 ) ( - x ^{2} + 9 b x + 9 )}{72}

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What is (-(x^2)/8+ax+1)(-(x^2)/9+bx+1) ?
The solution to (-(x^2)/8+ax+1)(-(x^2)/9+bx+1) is ((-x^2+8ax+8)(-x^2+9bx+9))/(72)