Chapter ISG, Problem 8.2.2P

a.

To determine

To expand each product

Answer to Problem 8.2.2P

  $8.79x^3+15.78x^2+8.51x^3+81.21x$ is the expanded product

Explanation of Solution

Given information:

  $-2.74x^2(3.21x-5.76)+8.27x(1.03x^3+9.82)$

Calculation:

The given equation is $-2.74x^2(3.21x-5.76)+8.27x(1.03x^3+9.82)$

Solving the equation,

= $(-2.74x^2)(3.21x)-5.76(-2.74x^2)+8.27x(1.03x^3)+9.82(8.27x)$

Multiplying,

= $(-2.74)(3.21)x^{2+1}+5.76(2.74)x^2+8.27(1.03)x^{1+2}+9.82(8.27)x$

So,

= $8.79x^3+15.78x^2+8.51x^3+81.21x$

Hence, $8.79x^3+15.78x^2+8.51x^3+81.21x$ is the expanded product

b.

To determine

To expand each product

Answer to Problem 8.2.2P

  $32.58y^5-24.92y^4+40.13y^3$ is the expanded product

Explanation of Solution

Given information:

  $5.28y^3(2.63y^2-4.72y+7.60)$

Calculation:

The given equation is $5.28y^3(2.63y^2-4.72y+7.60)$

Multiplying,

= $32.58y^{2+3}-24.92y^{3+1}+40.13y^3$

So,

= $32.58y^5-24.92y^4+40.13y^3$

Hence, $32.58y^5-24.92y^4+40.13y^3$ is the expanded product

c.

To determine

To expand each product

Answer to Problem 8.2.2P

Explanation of Solution

Given information:

  $-9.7x^4(5.3-4.7x^3)-8.9x^2(-4.1-6.2x^3)$

Calculation:

The given equation is $-9.7x^4(5.3-4.7x^3)-8.9x^2(-4.1-6.2x^3)$

Solving the equation,

= $-9.7x^4(5.3)-9.7x^4(-4.7x^3)-8.9x^2(-4.1)-8.9x^2(-6.2x^3)$

Multiplying,

= $-51.41x^4+45.59x^{4+3}+45.59x^2+55.18x^{2+5}$

So,

= $-51.41x^4+45.59x^7+45.59x^2+55.18x^7$

Hence, $-51.41x^4+100.77x^7+45.59x^2$ is the expanded product

d.

To determine

To expand each product

Answer to Problem 8.2.2P

0 is the expanded product.

Explanation of Solution

Given information:

  $-x^3(8-4x^3)-2x^2(2x^4-4x)$

Calculation:

The given equation is $-x^3(8-4x^3)-2x^2(2x^4-4x)$

Solving the equation,

= $-x^3(8)-x^3(-4x^3)-2x^2(2x^4)-2x^2(-4x)$

Multiplying,

= $-8x^3+4x^{3+3}-4x^{2+4}+8x^{2+1}$

So,

= $-8x^3+4x^6-4x^6+8x^3$

Hence, 0 is the expanded product