Chapter ISG, Problem 8.3.1P

a.

To determine

To write each expression as simplified polynomial

Answer to Problem 8.3.1P

  $12c^4+14c^3-6c^2+9c-6$ is simplified expression.

Explanation of Solution

Given:

  $(3c-2)(4c^2-c^3+3)$

Calculation:

The given expression is $(3c-2)(4c^2-c^3+3)$

Solving,

  = $3c(4c^2)+3c(c^3)+3c(3)-2(4c^2)+2(c^3)-6$

Multiplying,

  = $12c^{1+2}+12c^{1+3}+9c-6c^2+2c^3-6$

So,

  = $12c^3+12c^4+9c-6c^2+2c^3-6$

Adding terms,

  = $14c^3+12c^4+9c-6c^2-6$

Hence, $12c^4+14c^3-6c^2+9c-6$ is simplified expression.

b.

To determine

To write each expression as simplified polynomial

Answer to Problem 8.3.1P

  $7x^3-17x^{2}y+4x{y}^2+y^3$ is the simplified expression

Explanation of Solution

Given:

  $(5x-y)(3x^2-2xy)+(2x+y)(y^2-4x^2)$

Calculation:

The given equation is $(5x-y)(3x^2-2xy)+(2x+y)(y^2-4x^2)$

Multiplying terms,

  = $5x(3x^2)-2xy(5x)-y(3x^2)+2xy(y)+2x(y^2)-2x(4x^2)+y(y^2)-4x^2(y)$

Now,

  = $15x^3-10x^{2}y-3x^{2}y+2x{y}^2+2x{y}^2-8x^3+y^3-4x^{2}y$

Adding terms,

  = $15x^3-8x^3-10x^{2}y-3x^{2}y-4x^{2}y+2x{y}^2+2x{y}^2+y^3$

Hence,

  $7x^3-17x^{2}y+4x{y}^2+y^3$ is the simplified expression

c.

To determine

To write each expression as simplified polynomial

Answer to Problem 8.3.1P

  $-12x^2-24x+4x^4+8x^3$ is the simplified expression

Explanation of Solution

Given:

  $-2x(3-x^2)(2x+4)$

Calculation:

The given equation is $-2x(3-x^2)(2x+4)$

Multiplying,

  = $(-6x+2x^3)(2x+4)$

Now,

  = $-6x(2x+4)+2x^3(2x+4)$

Solving,

  = $-12x^2-24x+4x^4+8x^3$

Hence, $-12x^2-24x+4x^4+8x^3$ is the simplified expression

d.

To determine

To write each expression as simplified polynomial

Answer to Problem 8.3.1P

Explanation of Solution

Given:

  $(z-1)(2-z)(z+1)$

Calculation:

The equation is $(z-1)(2-z)(z+1)$

Solving,

  = $(2z-z-2+z)(z+1)$

So,

  = $(2z-2)(z+1)$

Multiplying,

  = $2z(z+1)-2(z+1)$

Now,

  = $2z^2+2z-2z-2$

Subtracting terms,

  = $2z^2-2$

Hence, $2z^2-2$ is the simplified form