Multiply. \[ \left(8 x^{2}-4 x+5\right)(5 x+1) \]
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Bonus Knowledge
To multiply the expressions \((8x^{2}-4x+5)(5x+1)\), we can use the distributive property, also known as the FOIL method for binomials. 1. First, distribute \(5x\) to each term in the first polynomial: \[ 5x \cdot 8x^2 = 40x^3, \] \[ 5x \cdot (-4x) = -20x^2, \] \[ 5x \cdot 5 = 25x. \] 2. Next, distribute \(1\) to each term in the first polynomial: \[ 1 \cdot 8x^2 = 8x^2, \] \[ 1 \cdot (-4x) = -4x, \] \[ 1 \cdot 5 = 5. \] 3. Now, combine all the results: \[ 40x^3 + (-20x^2 + 8x^2) + (25x - 4x) + 5. \] 4. Simplify by combining like terms: \[ 40x^3 + (-12x^2) + (21x) + 5. \] Thus, the final result is: \[ \boxed{40x^3 - 12x^2 + 21x + 5}. \]
