(25a2%2B10ab%2B4b2)-(2a%2B5b)(4a2-10ab%2B25b2).jpeg "(5a-2b)(25a2+10ab+4b2)-(2a+5b)(4a2-10ab+25b2)")
Simplifying the Expression (5a-2b)(25a^2+10ab+4b^2)-(2a+5b)(4a^2-10ab+25b^2)
This expression involves two sets of parentheses multiplied together, then subtracted. To simplify this, we can use the distributive property and then combine like terms.
Applying the Distributive Property
First, we distribute the terms in the first set of parentheses to the terms in the second set:
(5a-2b)(25a^2+10ab+4b^2) = (5a * 25a^2) + (5a * 10ab) + (5a * 4b^2) - (2b * 25a^2) - (2b * 10ab) - (2b * 4b^2)
Similarly, we distribute the terms in the third set of parentheses to the terms in the fourth set:
(2a+5b)(4a^2-10ab+25b^2) = (2a * 4a^2) + (2a * -10ab) + (2a * 25b^2) + (5b * 4a^2) + (5b * -10ab) + (5b * 25b^2)
Combining Like Terms
Now we can simplify by combining like terms:
125a^3 + 50a^2b + 20ab^2 - 50a^2b - 20ab^2 - 8b^3 - 8a^3 - 20a^2b + 50ab^2 + 20a^2b - 50ab^2 + 125b^3
Notice that some terms cancel each other out:
125a^3 - 8b^3 - 8a^3 + 125b^3
Finally, we combine the remaining terms:
117a^3 + 117b^3
Conclusion
The simplified expression for (5a-2b)(25a^2+10ab+4b^2)-(2a+5b)(4a^2-10ab+25b^2) is 117a^3 + 117b^3.