12. \(-2x^2 - (4x^2 + 5x) - 1\)
\(= -2x^2 - 4x^2 - 5x - 1\)
\(= (-2x^2 - 4x^2) - 5x - 1\)
\(= -6x^2 - 5x - 1\)
Answer: \(\mathbf{-6x^2 - 5x - 1}\)
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Teacher Answer Key Distribution & Polynomial Subtraction • Page 3
Focused Review: Types 9–12
13. \(-2(3x - 5) - 3(x + 4)\)
\(= -6x + 10 - 3x - 12\)
\(= (-6x - 3x) + (10 - 12)\)
\(= -9x - 2\)
Answer: \(\mathbf{-9x - 2}\)
14. \(5(2x - 1) - 4(3x - 6)\)
\(= 10x - 5 - 12x + 24\)
\(= (10x - 12x) + (-5 + 24)\)
\(= -2x + 19\)
Answer: \(\mathbf{-2x + 19}\)
15. \(5x^2 - (8x^2 + 3x) - 7\)
\(= 5x^2 - 8x^2 - 3x - 7\)
\(= (5x^2 - 8x^2) - 3x - 7\)
\(= -3x^2 - 3x - 7\)
Answer: \(\mathbf{-3x^2 - 3x - 7}\)
16. \(7x^2 - (3x^2 - 4x) - 9\)
\(= 7x^2 - 3x^2 + 4x - 9\)
\(= (7x^2 - 3x^2) + 4x - 9\)
\(= 4x^2 + 4x - 9\)
Answer: \(\mathbf{4x^2 + 4x - 9}\)
17. \(-4x^2 - (2x^2 + 6x) + 5\)
\(= -4x^2 - 2x^2 - 6x + 5\)
\(= (-4x^2 - 2x^2) - 6x + 5\)
\(= -6x^2 - 6x + 5\)
Answer: \(\mathbf{-6x^2 - 6x + 5}\)
18. \(8x^2 - (5x^2 - 7x) - 2\)
\(= 8x^2 - 5x^2 + 7x - 2\)
\(= (8x^2 - 5x^2) + 7x - 2\)
\(= 3x^2 + 7x - 2\)
Answer: \(\mathbf{3x^2 + 7x - 2}\)
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Teacher Answer Key Monomial Distribution & Review • Page 4
Original: #4: \(x^4 + 8x^3 - 4x^2 + 2x\)
19. \(x(x^3 + 5x^2 - 6x + 4)\)
\(= x(x^3) + x(5x^2) - x(6x) + x(4)\)
\(= x^4 + 5x^3 - 6x^2 + 4x\)
Answer: \(\mathbf{x^4 + 5x^3 - 6x^2 + 4x}\)
20. \(2x(3x^3 - 4x^2 + 7x - 5)\)
\(= 2x(3x^3) - 2x(4x^2) + 2x(7x) - 2x(5)\)
\(= 6x^4 - 8x^3 + 14x^2 - 10x\)
Answer: \(\mathbf{6x^4 - 8x^3 + 14x^2 - 10x}\)
21. \(x(2x^3 - 9x^2 + 3x - 8)\)
\(= x(2x^3) - x(9x^2) + x(3x) - x(8)\)
\(= 2x^4 - 9x^3 + 3x^2 - 8x\)
Answer: \(\mathbf{2x^4 - 9x^3 + 3x^2 - 8x}\)
22. \(3x(2x^3 - 4x^2 + 5x - 1)\)
\(= 3x(2x^3) - 3x(4x^2) + 3x(5x) - 3x(1)\)
\(= 6x^4 - 12x^3 + 15x^2 - 3x\)
Answer: \(\mathbf{6x^4 - 12x^3 + 15x^2 - 3x}\)
23. \(f - g\) for \(f=3x^2-4x+2,\; g=5x^2+2x-7\)
\((f - g)(x) = (3x^2 - 4x + 2) - (5x^2 + 2x - 7)\)
\(= 3x^2 - 4x + 2 - 5x^2 - 2x + 7\)
\(= -2x^2 - 6x + 9\)
Answer: \(\mathbf{-2x^2 - 6x + 9}\)
24. \(f + g\) for \(f=2x^2-6x-1,\; g=-4x^2+3x+8\)
\((f + g)(x) = (2x^2 - 6x - 1) + (-4x^2 + 3x + 8)\)
\(= (2x^2 - 4x^2) + (-6x + 3x) + (-1 + 8)\)
\(= -2x^2 - 3x + 7\)
Answer: \(\mathbf{-2x^2 - 3x + 7}\)
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