QuestionCalculate $\left(7 x^{5} y^{2}+5 x^{4} y^{3}\right)\left(7 x^{5} y^{2}-5 x^{4} y^{3}\right)$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\left(7 x^{5} y^{}+5 x^{4} y^{3}\right)\left(7 x^{5} y^{}-5 x^{4} y^{3}\right)$ . We are asked to simplify this expression.

STEP 2

We can recognize the given expression as a difference of squares. The difference of squares is a special case of the identity $a^{2}-b^{2}=(a+b)(a-b)$ .

STEP 3

In our case, $a$ is $7 x^{5} y^{2}$ and $b$ is $5 x^{} y^{3}$ . So, we can rewrite the expression as $a^{2}-b^{2}$ .

STEP 4

Substitute the values of $a$ and $b$ into the difference of squares formula.
$a^{2}-b^{2} = (7 x^{} y^{2})^{2} - ( x^{4} y^{3})^{2}$

STEP 5

Calculate the square of $7 x^{5} y^{2}$ and $5 x^{4} y^{3}$ .
$a^{2}-b^{2} = (49 x^{10} y^{4}) - (25 x^{8} y^{})$

STEP 6

The expression is now simplified to $49 x^{10} y^{4} -25 x^{8} y^{6}$ .
So, $\left( x^{5} y^{2}+5 x^{4} y^{3}\right)\left( x^{5} y^{2}-5 x^{4} y^{3}\right) =49 x^{10} y^{4} -25 x^{8} y^{6}$ .

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QuestionCalculate $\left(7 x^{5} y^{2}+5 x^{4} y^{3}\right)\left(7 x^{5} y^{2}-5 x^{4} y^{3}\right)$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\left(7 x^{5} y^{}+5 x^{4} y^{3}\right)\left(7 x^{5} y^{}-5 x^{4} y^{3}\right)$ . We are asked to simplify this expression.

STEP 2

We can recognize the given expression as a difference of squares. The difference of squares is a special case of the identity $a^{2}-b^{2}=(a+b)(a-b)$ .

STEP 3

In our case, $a$ is $7 x^{5} y^{2}$ and $b$ is $5 x^{} y^{3}$ . So, we can rewrite the expression as $a^{2}-b^{2}$ .

STEP 4

Substitute the values of $a$ and $b$ into the difference of squares formula.
$a^{2}-b^{2} = (7 x^{} y^{2})^{2} - ( x^{4} y^{3})^{2}$

STEP 5

Calculate the square of $7 x^{5} y^{2}$ and $5 x^{4} y^{3}$ .
$a^{2}-b^{2} = (49 x^{10} y^{4}) - (25 x^{8} y^{})$

STEP 6

The expression is now simplified to $49 x^{10} y^{4} -25 x^{8} y^{6}$ .
So, $\left( x^{5} y^{2}+5 x^{4} y^{3}\right)\left( x^{5} y^{2}-5 x^{4} y^{3}\right) =49 x^{10} y^{4} -25 x^{8} y^{6}$ .

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QuestionCalculate (7x5y2+5x4y3)(7x5y2−5x4y3)\left(7 x^{5} y^{2}+5 x^{4} y^{3}\right)\left(7 x^{5} y^{2}-5 x^{4} y^{3}\right)(7x5y2+5x4y3)(7x5y2−5x4y3).

Studdy Solution

STEP 1

Assumptions1. We are given the expression (7x5y+5x4y3)(7x5y−5x4y3)\left(7 x^{5} y^{}+5 x^{4} y^{3}\right)\left(7 x^{5} y^{}-5 x^{4} y^{3}\right)(7x5y+5x4y3)(7x5y−5x4y3). We are asked to simplify this expression.

STEP 2

We can recognize the given expression as a difference of squares. The difference of squares is a special case of the identity a2−b2=(a+b)(a−b)a^{2}-b^{2}=(a+b)(a-b)a2−b2=(a+b)(a−b).

STEP 3

In our case, aaa is 7x5y27 x^{5} y^{2}7x5y2 and bbb is 5xy35 x^{} y^{3}5xy3. So, we can rewrite the expression as a2−b2a^{2}-b^{2}a2−b2.

STEP 4

Substitute the values of aaa and bbb into the difference of squares formula.a2−b2=(7xy2)2−(x4y3)2a^{2}-b^{2} = (7 x^{} y^{2})^{2} - ( x^{4} y^{3})^{2}a2−b2=(7xy2)2−(x4y3)2

STEP 5

Calculate the square of 7x5y27 x^{5} y^{2}7x5y2 and 5x4y35 x^{4} y^{3}5x4y3.a2−b2=(49x10y4)−(25x8y)a^{2}-b^{2} = (49 x^{10} y^{4}) - (25 x^{8} y^{})a2−b2=(49x10y4)−(25x8y)

STEP 6

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QuestionCalculate $\left(7 x^{5} y^{2}+5 x^{4} y^{3}\right)\left(7 x^{5} y^{2}-5 x^{4} y^{3}\right)$ .

Assumptions1. We are given the expression $\left(7 x^{5} y^{}+5 x^{4} y^{3}\right)\left(7 x^{5} y^{}-5 x^{4} y^{3}\right)$ . We are asked to simplify this expression.

We can recognize the given expression as a difference of squares. The difference of squares is a special case of the identity $a^{2}-b^{2}=(a+b)(a-b)$ .

In our case, $a$ is $7 x^{5} y^{2}$ and $b$ is $5 x^{} y^{3}$ . So, we can rewrite the expression as $a^{2}-b^{2}$ .

Substitute the values of $a$ and $b$ into the difference of squares formula.
$a^{2}-b^{2} = (7 x^{} y^{2})^{2} - ( x^{4} y^{3})^{2}$

Calculate the square of $7 x^{5} y^{2}$ and $5 x^{4} y^{3}$ .
$a^{2}-b^{2} = (49 x^{10} y^{4}) - (25 x^{8} y^{})$