Chapter ISG, Problem 8.4STP

i.

To determine

To simplify the expression

Answer to Problem 8.4STP

Simplified expression is $6g^3+10g-3g$

Explanation of Solution

Given:

  $(6g^3-4g+g^2)+(9g^2+g)$

Calculation:

The given expression is $(6g^3-4g+g^2)+(9g^2+g)$

Solving the equation,

  = $6g^3+(9g^2+g^2)+(-4g+g)$

So,

  = $6g^3+10g-3g$

Hence, simplified expression is $6g^3+10g-3g$

ii.

To determine

To simplify the expression

Answer to Problem 8.4STP

  $5x^{2}y-x^2{y}^2+10x{y}^2$ is simplified expression

Explanation of Solution

Given:

  $(5x^{2}y+3x{y}^2)-(x^2{y}^2-7x{y}^2)$

Calculation:

Thegiven expression is $(5x^{2}y+3x{y}^2)-(x^2{y}^2-7x{y}^2)$

Solving the equation,

  = $5x^{2}y+3x{y}^2-x^2{y}^2+7x{y}^2$

So,

  = $5x^{2}y-x^2{y}^2+10x{y}^2$

Hence, $5x^{2}y-x^2{y}^2+10x{y}^2$ is simplified expression

iii.

To determine

To simplify the expression

Answer to Problem 8.4STP

  $18x^2+8y^2+15xy+x$ is simplified expression

Explanation of Solution

Given:

  $(-2x^2+8y^2-4x)+5x(3y+4x+1)$

Calculation:

The given expression $(-2x^2+8y^2-4x)+5x(3y+4x+1)$

Solving the expression,

  = $(-2x^2+8y^2-4x)+(15xy+20x^2+5x)$

So,

  = $18x^2+8y^2+15xy+x$

Hence, $18x^2+8y^2+15xy+x$ is simplified expression

ii.

To determine

To simplify the expression

Answer to Problem 8.4STP

  $43a^2+29a$ is simplified expression.

Explanation of Solution

Given:

  $7a(4a+5)+3(5a^2-2a)$

Calculation:

The given expression is $7a(4a+5)+3(5a^2-2a)$

Solving the expression,

  = $7a(4a)+7a(5)+3(5a^2)-3(2a)$

So,

  = $28a^2+35a+15a^2-6a$

Adding like terms,

  = $43a^2+29a$

Hence, $43a^2+29a$ is simplified expression.