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Simplify Expressions - Please Help this is Important

by Brock10
(U.S.)










































Simplify the expressions below. Write the final product in standard form and show your work to receive full credit.

2x4(4x2 + 3x + 1)
(4x – 3)(2x2 – 7x + 1)
(x2 + 4x – 3)(2x2 + x + 6)

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Mar 16, 2012
Simplify Expressions
by: Staff


Question:

by Brock10
(U.S.)


Simplify the expressions below. Write the final product in standard form and show your work to receive full credit.

2x4(4x2 + 3x + 1)
(4x – 3)(2x2 – 7x + 1)
(x2 + 4x – 3)(2x2 + x + 6)


Answer:


I. 2x4(4x2 + 3x + 1)


= 2x⁴(4x² + 3x + 1)

= (2x⁴)*(4x²) + (2x⁴)*(3x¹) + (2x⁴)*(1)

= (2*4)*(x⁴*x²) + (2*3)*(x⁴*x¹) + (2*1)*(x⁴)

= (8)*(x⁴*x²) + (6)*(x⁴*x¹) + (2)*(x⁴)

= (8)*(x⁴⁺²) + (6)*(x⁴⁺¹) + (2)*(x⁴)

= (8)*(x⁶) + (6)*(x⁵) + (2)*(x⁴)

>>> FINAL = 8x⁶ + 6x⁵ + 2x⁴



II. (4x – 3)(2x2 – 7x + 1)

= (4x¹ - 3)(2x² - 7x¹ + 1)

= (4x¹ - 3)*(2x²) + (4x¹ - 3)*(-7x¹) + (4x¹- 3)*(1)

= (4x¹)*(2x²) - 3*(2x²) + (4x¹)*(-7x¹) - (3)*(-7x¹) + (4x¹)*(1) - (3)*(1)

= (4*2)*(x¹*x²) - (3*2)*x² + [4*(-7)]*(x¹*x¹) - [3*(-7)]*x¹ + (4*1)*x¹ - (3)*(1)

= (8)*(x¹*x²) - (6)*x² + (-28)*(x¹*x¹) - (-21)*x¹ + 4*x¹ - 3

= (8)*(x¹⁺²) - (6)*x² + (-28)*(x¹⁺¹) - (-21)*x¹ + 4*x¹ - 3

= (8)*(x³) - (6)*x² + (-28)*(x²) - (-21)*x¹ + 4*x¹ - 3

= 8x³ - 6x² - 28x² + 21x + 4x - 3

= 8x³ + (- 6x² - 28x²) + (21x + 4x) - 3

= 8x³ + (- 34x²) + (25x) – 3

>>> FINAL = 8x³ - 34x² + 25x - 3




III. (x2 + 4x - 3)(2x2 + x + 6)

= (x² + 4x¹ - 3)(2x² + x¹ + 6)

= (x²)*(2x²) + (x²)*(x¹) + (x²)*(6) + (4x¹)*(2x²) + (4x¹)*(x¹) + (4x¹)*(6) + (-3)*(2x²) + (-3)*(x¹) + (-3)*(6)

= (1*2)*(x²*x²) + (1*1)*(x²*x¹) + (1*6)(x²) + (4*2)*(x¹*x²) + (4*1)*(x¹*x¹) + (4*6)*(x¹) + (-3*2)*(x²) + (-3*1)*(x¹) + (-3*6)

= (2)*(x²*x²) + (1)*(x²*x¹) + (6)(x²) + (8)*(x¹*x²) + (4)*(x¹*x¹) + (24)*(x¹) + (-6)*(x²) + (-3)*(x¹) + (-18)

= (2)*(x²⁺²) + (1)*(x²⁺¹) + (6)(x²) + (8)*(x¹⁺²) + (4)*(x¹⁺¹) + (24)*(x¹) + (-6)*(x²) + (-3)*(x¹) + (-18)

= (2)*(x⁴) + (1)*(x³) + (6)(x²) + (8)*(x³) + (4)*(x²) + (24)*(x¹) + (-6)*(x²) + (-3)*(x¹) + (-18)

= 2x⁴ + x³ + 6x² + 8x³ + 4x² + 24x¹ - 6x² - 3x¹ - 18

= 2x⁴ + x³ + 8x³ + 6x² + 4x² - 6x² + 24x¹ - 3x¹ - 18

= 2x⁴ + (x³ + 8x³) + (6x² + 4x² - 6x²) + (24x¹ - 3x¹) - 18

= 2x⁴ + (9x³) + (4x²) + (21x¹) - 18

= 2x⁴ + 9x³ + 4x² + 21x – 18

>>> FINAL = 2x⁴ + 9x³ + 4x² + 21x - 18





Thanks for writing.

Staff
www.solving-math-problems.com



Dec 02, 2014
answer NEW
by: Anonymous

Simplify the expression 4x(2x2 − 7x + 3).

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