body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

8. Differences of Squares

Continue to next subchapter

Exercise 16 Page 61

The formula to factor the difference of two squares is a^2-b^2=(a+b)(a-b).

(r^2+k^2)(r+k)(r-k)

Practice makes perfect

Look closely at the expression r^4-k^4. It can be expressed as the difference of two perfect squares.

r^4-k^4

Write as a power

(r^2)^2-(k^2)^2

Recall the formula to factor a difference of squares. a^2- b^2 ⇔ ( a+ b)( a- b) We can apply this formula to our expression. ( r^2)^2-( k^2)^2 ⇔ ( r^2+ k^2)( r^2- k^2) Now, let's take a look at the expression r^2-k^2. It is already written as a difference of two perfect squares, so we can use the above formula once again. (r^2+k^2)( r^2- k^2) ⇕ (r^2+k^2)( r+ k)( r- k)

Checking Our Answer

Check your answer ✓

We can apply the Distributive Property and compare the result with the given expression.

(r^2+k^2)(r + k) (r - k)

Distribute r^2+k^2

(r(r^2+k^2) + k(r^2+k^2)) (r - k)

▼

Distribute r & k

Distribute r

(r^3+k^2r + k(r^2+k^2))(r - k)

Distribute k

(r^3+k^2r+kr^2+k^3)(r-k)

Distribute (r-k)

r^3(r-k) + k^2r(r-k) + kr^2(r-k) + k^3(r-k)

▼

Simplify

Distribute r^3

r^4-kr^3 + k^2r(r-k) + kr^2(r-k) + k^3(r-k)

Distribute k^2r

r^4-kr^3 + k^2r^2-k^3r + kr^2(r-k) + k^3(r-k)

Distribute kr^2

r^4-kr^3 + k^2r^2-k^3r + kr^3-k^2r^2 + k^3(r-k)

Distribute k^3

r^4-kr^3 + k^2r^2-k^3r + kr^3-k^2r^2 + k^3r -k^4

Add and subtract terms

r^4-k^4

After applying the Distributive Property and simplifying, the result is the same as the given expression. Therefore, we can be sure our solution is correct!

Subchapter links

Exercises p.60-63