can someone explain how I would simplify (3a4 - 2a2 + 5a - 10)(2a4 + 4a2 + 5a - 2)? can anyone help? The #'s that come directly after a letter is the exponent.
I just need help understanding how to simplify problems like this...
3a^4(2a^4+4a^2+5a-2)
-2a^2(2a^4+4a^2+5a-2)
+5a(2a^4+4a^2+5a-2)
-10(2a^4+4a^2+5a-2)
6a^8 + 12a^6 + 15a^5 - 6a^4
-4a^6 - 8a^4 - 10a^3 + 4a^2
+10a^5 + 20a^3 + 25a^2 - 10a
-20a^4 - 40a^2 - 50a + 20
6a^8 + 8a^6 +25a^5 -34a^4 +10a^3 - 11a^2 - 60a + 20
feel free to double-check my math, or using wolframaplha
no i need it to be shorter?.
Factor completely. 25a^2-64
To simplify the expression (3a^4 - 2a^2 + 5a - 10)(2a^4 + 4a^2 + 5a - 2), we first need to understand how to multiply monomials (a single term) and polynomials (an expression with two or more terms).
The given expression is in the form of (a + b)(c + d), which can be simplified using the distributive property of multiplication over addition. To simplify it, follow these steps:
1. Multiply the terms of the first polynomial by each term of the second polynomial. Start by multiplying the first term of the first polynomial by each term of the second polynomial:
(3a^4)(2a^4) + (3a^4)(4a^2) + (3a^4)(5a) + (3a^4)(-2)
2. Continue multiplying each remaining term of the first polynomial by each term of the second polynomial. In this case, you need to multiply the first term of the first polynomial by each remaining term in the second polynomial:
(-2a^2)(2a^4) + (-2a^2)(4a^2) + (-2a^2)(5a) + (-2a^2)(-2)
3. Proceed to the next term of the first polynomial and multiply it by each term of the second polynomial:
(5a)(2a^4) + (5a)(4a^2) + (5a)(5a) + (5a)(-2)
4. Finally, multiply the last term of the first polynomial by each term of the second polynomial:
(-10)(2a^4) + (-10)(4a^2) + (-10)(5a) + (-10)(-2)
5. Simplify each multiplication operation, combining like terms if necessary. For example, a^4 multiplied by a^4 equals a^(4 + 4) = a^8, and 3a^4 multiplied by 2 equals 6a^4.
After performing all the multiplications and simplifications, combine like terms by adding or subtracting coefficients with the same exponent. The final answer will be the simplified form of the expression you started with.
If you have specific coefficients and exponents, feel free to share them, and I can guide you through the simplification process step-by-step.