Chapter ISG, Problem 8.2.1P

a.

To determine

To expand each product

Answer to Problem 8.2.1P

  $5x^2-5x^3+15x^4$ is the expanded product.

Explanation of Solution

Given:

  $5x^2(1-x+3x^2)$

Calculation:

The given equation is $5x^2(1-x+3x^2)$

Solving,

  = $5x^2(1)-x(5x^2)+5x^2(3x^2)$

Multiplying = $5x^2-5x^{2+1}+5(3)x^{2+2}$

So,

  = $5x^2-5x^3+15x^4$

Hence, $5x^2-5x^3+15x^4$ is the expanded product.

b.

To determine

To expand each product

Answer to Problem 8.2.1P

  $-7z^6+35z^5+12z^3-2z^2$ is the expanded product.

Explanation of Solution

Given:

  $-7z^5(z-5)+2z(6z^2-z)$

Calculation:

The given equation is $-7z^5(z-5)+2z(6z^2-z)$

Solving,

  = $-7z^5(z)+(-5)(-7z^5)+2z(6z^2)-(2z)(-z)$

Multiplying,

  = $-7z^{5+1}+35z^5+12z^{2+1}-2z^{1+1}$

So,

  = $-7z^6+35z^5+12z^3-2z^2$

Hence, $-7z^6+35z^5+12z^3-2z^2$ is the expanded product.

c.

To determine

To expand each product

Answer to Problem 8.2.1P

  $3b^5-6b^5-24b^5+36b^6$ is the expanded product.

Explanation of Solution

Given:

  $-3b^4(-b+2b)-12b^2(2b^3-3b^4)$

Calculation:

The given equation is $-3b^4(-b+2b)-12b^2(2b^3-3b^4)$

Solving,

  = $-3b^4(-b)+(-3b^4)(2b)-12b^2(2b^3)-12b^2(-3b^4)$

Multiplying equation,

  = $3b^{4+1}-6b^{4+1}-24b^5+36b^{2+4}$

So,

  = $3b^5-6b^5-24b^5+36b^6$

Hence, $3b^5-6b^5-24b^5+36b^6$ is the expanded product.

d.

To determine

To expand each product

Answer to Problem 8.2.1P

  $6h-2h^4+{14}^2-8h^2+2h^3$ is the expanded product

Explanation of Solution

Given:

  $2h(3-h^3+7h)-2h^2(4+h)$

Calculation:

The given equation is $2h(3-h^3+7h)-2h^2(4+h)$

Solving the equation,

  = $2h(3)+2h(-h^3)+2h(7h)-2h^2(4)+2h^2(h)$

Multiplying,

  = $6h-2h^{3+1}+{14}^{1+1}-8h^2+2h^{2+1}$

So,

  = $6h-2h^4+{14}^2-8h^2+2h^3$

Hence, $6h-2h^4+{14}^2-8h^2+2h^3$ is the expanded product