Question Find the expression for the product of $(p-10 q)$ and $(p+10 q)$ .

Studdy Solution

STEP 1

Assumptions
1. We are given a binomial expression in the form $(a - b)(a + b)$ .
2. We need to simplify the expression using the difference of squares formula.
3. The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ .

STEP 2

Identify the terms $a$ and $b$ in the given expression $(p-10q)(p+10q)$ .
$a = p$ $b = 10q$

STEP 3

Apply the difference of squares formula to the given expression.
$(p-10q)(p+10q) = a^2 - b^2$

STEP 4

Substitute the identified terms $a$ and $b$ into the formula.
$(p-10q)(p+10q) = p^2 - (10q)^2$

STEP 5

Square the term $10q$ .
$(10q)^2 = 100q^2$

STEP 6

Substitute the squared term back into the expression.
$(p-10q)(p+10q) = p^2 - 100q^2$

STEP 7

The expression is now simplified.
$(p-10q)(p+10q) = p^2 - 100q^2$
The simplified form of the given expression is $p^2 - 100q^2$ .

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Question Find the expression for the product of $(p-10 q)$ and $(p+10 q)$ .

Studdy Solution

STEP 1

Assumptions
1. We are given a binomial expression in the form $(a - b)(a + b)$ .
2. We need to simplify the expression using the difference of squares formula.
3. The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ .

STEP 2

Identify the terms $a$ and $b$ in the given expression $(p-10q)(p+10q)$ .
$a = p$ $b = 10q$

STEP 3

Apply the difference of squares formula to the given expression.
$(p-10q)(p+10q) = a^2 - b^2$

STEP 4

Substitute the identified terms $a$ and $b$ into the formula.
$(p-10q)(p+10q) = p^2 - (10q)^2$

STEP 5

Square the term $10q$ .
$(10q)^2 = 100q^2$

STEP 6

Substitute the squared term back into the expression.
$(p-10q)(p+10q) = p^2 - 100q^2$

STEP 7

The expression is now simplified.
$(p-10q)(p+10q) = p^2 - 100q^2$
The simplified form of the given expression is $p^2 - 100q^2$ .

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Question Find the expression for the product of (p−10q)(p-10 q)(p−10q) and (p+10q)(p+10 q)(p+10q).

Studdy Solution

STEP 1

Assumptions1. We are given a binomial expression in the form (a−b)(a+b)(a - b)(a + b)(a−b)(a+b).2. We need to simplify the expression using the difference of squares formula.3. The difference of squares formula is a2−b2=(a−b)(a+b)a^2 - b^2 = (a - b)(a + b)a2−b2=(a−b)(a+b).

STEP 2

Identify the terms aaa and bbb in the given expression (p−10q)(p+10q)(p-10q)(p+10q)(p−10q)(p+10q).a=pa = pa=p b=10qb = 10qb=10q

STEP 3

Apply the difference of squares formula to the given expression.(p−10q)(p+10q)=a2−b2 (p-10q)(p+10q) = a^2 - b^2 (p−10q)(p+10q)=a2−b2

STEP 4

Substitute the identified terms aaa and bbb into the formula.(p−10q)(p+10q)=p2−(10q)2 (p-10q)(p+10q) = p^2 - (10q)^2 (p−10q)(p+10q)=p2−(10q)2

STEP 5

Square the term 10q10q10q.(10q)2=100q2 (10q)^2 = 100q^2 (10q)2=100q2

STEP 6

Substitute the squared term back into the expression.(p−10q)(p+10q)=p2−100q2 (p-10q)(p+10q) = p^2 - 100q^2 (p−10q)(p+10q)=p2−100q2

STEP 7

The expression is now simplified.(p−10q)(p+10q)=p2−100q2 (p-10q)(p+10q) = p^2 - 100q^2 (p−10q)(p+10q)=p2−100q2The simplified form of the given expression is p2−100q2p^2 - 100q^2p2−100q2.

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Question Find the expression for the product of $(p-10 q)$ and $(p+10 q)$ .

Assumptions
1. We are given a binomial expression in the form $(a - b)(a + b)$ .
2. We need to simplify the expression using the difference of squares formula.
3. The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ .

Identify the terms $a$ and $b$ in the given expression $(p-10q)(p+10q)$ .
$a = p$ $b = 10q$

Apply the difference of squares formula to the given expression.
$(p-10q)(p+10q) = a^2 - b^2$

Substitute the identified terms $a$ and $b$ into the formula.
$(p-10q)(p+10q) = p^2 - (10q)^2$

Square the term $10q$ .
$(10q)^2 = 100q^2$

Substitute the squared term back into the expression.
$(p-10q)(p+10q) = p^2 - 100q^2$

The expression is now simplified.
$(p-10q)(p+10q) = p^2 - 100q^2$
The simplified form of the given expression is $p^2 - 100q^2$ .