Chapter ISG, Problem 8.4.1P

a.

To determine

Expand the expression by using pattern

Answer to Problem 8.4.1P

The pattern applied is square of difference. $x^2+25-10x$ is expanded form.

Explanation of Solution

Given:

  ${(x-5)}^2$

Calculation:

The pattern applied is square of difference which is

  ${(a-b)}^2=a^2+b^2-2ab$

Substituting values,

  ${(x-5)}^2$ = $x^2+5^2-2(x)(5)$

Solving,

  = $x^2+25-10x$

Hence, it is the expanded form.

b.

To determine

Expand the expression by using pattern

Answer to Problem 8.4.1P

The pattern applied is square of sum. $y^2+4+4y$ is expanded form.

Explanation of Solution

Given:

  ${(y+2)}^2$

Calculation:

The pattern applied is square of sum which is

  ${(a+b)}^2=a^2+b^2-2ab$

Substituting values,

  ${(y+2)}^2=y^2+2^2+2(y)(2)$

Solving,

  = $y^2+4+4y$

Hence, it is the expanded form.

c.

To determine

Expand the expression by using pattern

Answer to Problem 8.4.1P

The pattern applied is square of difference. $4z^2+9-12z$ is the expanded form.

Explanation of Solution

Given:

  ${(2z-3)}^2$

Calculation:

The pattern applied is square of difference which is

  ${(a-b)}^2=a^2+b^2-2ab$

Substituting values,

  ${(2z-3)}^2={(2z)}^2+{(3)}^2-2(2z)(3)$

Solving,

  = $4z^2+9-12z$

Hence, it is the expanded form.

d.

To determine

Expand the expression by using pattern

Answer to Problem 8.4.1P

The pattern applied is square of difference, $a^2+4+4a$ is the expanded form

Explanation of Solution

Given:

  ${(-a-2)}^2$

Calculation:

The pattern applied is square of difference which is

  ${(a-b)}^2=a^2+b^2-2ab$

Substituting values,

  ${(-a-2)}^2={(-a)}^2+{(2)}^2-2(-a)(2)$

Solving,

  = $a^2+4+4a$

Hence, it is the expanded form.

e.

To determine

Expand the expression by using pattern $4b^2-9$

Answer to Problem 8.4.1P

The pattern is product of sum and difference of two terms.

Explanation of Solution

Given:

  $(2b-3)(2b+3)$

Calculation:

The pattern is product of sum and difference of two terms.

( $a+b)(a-b)=a^2-b^2$

Substituting value,

  $(2b-3)(2b+3)={(2b)}^2-3^2$

Solving,

  $4b^2-9$

Hence, it is the expanded form

f.

To determine

Expand the expression by using pattern

Answer to Problem 8.4.1P

The pattern is product of sum and difference of two terms. $16n^2-4m^2$ is the expanded form

Explanation of Solution

Given:

  $(4n-2m)(4n+2m)$

Calculation:

The pattern is product of sum and difference of two terms.

( $a+b)(a-b)=a^2-b^2$

Substituting value,

  $(4n-2m)(4n+2m)={(4n)}^2-{(2m)}^2$

Solving,

  $16n^2-4m^2$

Hence, it is the expanded form