For questions 17-21, simplify the expression.
17. 8t^5 x 8t^5
18. -x(6x -7)
19. 5k^2(-6k^2-2k+6)
20. (3k+2)(k-3)
21. (-3y+2)(y+3)
Please help
I would be happy to check your answers.
Remember when multiplying you multiply the coefficients and add the exponents.
4x^3 x 5x^4 = 20x^7
for 18 and 19 you will use the distributive property.
Multiply what is in front times each term inside the ( )
use the rule stated above.
Remember an x is really x^1
for 20 and 21
multiply 3k times k and -3
multiply 2 times k and -3
combine like terms.
Like terms have the same exponents.
ex: 3x^4 + 5x^4 = 8x^4
Sure, I can help you with those simplifications. Here are the step-by-step solutions:
17. To simplify the expression 8t^5 * 8t^5, you can multiply the coefficients (8 * 8) and combine the variables with the same base (t^5 * t^5). The final simplified expression is 64t^(5+5), which simplifies to 64t^10.
18. To simplify the expression -x(6x - 7), you can distribute the negative sign first, which gives you -6x^2 + 7x.
19. To simplify the expression 5k^2(-6k^2 - 2k + 6), you can distribute the 5k^2 into each term inside the parentheses. This gives you -30k^4 - 10k^3 + 30k^2.
20. To simplify the expression (3k + 2)(k - 3), you can use the distributive property. Multiply 3k with each term inside the other parentheses and then multiply 2 with each term inside the other parentheses. This gives you 3k * k - 3k * 3 + 2 * k - 2 * 3. The simplified expression is 3k^2 - 9k + 2k - 6, which simplifies to 3k^2 - 7k - 6.
21. To simplify the expression (-3y + 2)(y + 3), you can use the distributive property. Multiply -3y with each term inside the other parentheses and then multiply 2 with each term inside the other parentheses. This gives you -3y * y - 3y * 3 + 2 * y + 2 * 3. The simplified expression is -3y^2 - 9y + 2y + 6, which simplifies to -3y^2 - 7y + 6.
I hope this helps! Let me know if you have any more questions.
Sure! I'd be happy to help you simplify these expressions. Here's how you can approach each one:
17. To simplify the expression 8t^5 x 8t^5, you multiply the coefficients (numbers) and add the exponents of the variables. In this case, 8 x 8 is 64, and t^5 x t^5 is t^(5+5) = t^10. So the simplified expression is 64t^10.
18. To simplify the expression -x(6x -7), you distribute the -x to every term inside the parentheses. This means multiplying -x by each term separately. In this case, you get -6x^2 + 7x. So the simplified expression is -6x^2 + 7x.
19. To simplify the expression 5k^2(-6k^2-2k+6), you distribute the 5k^2 to every term inside the parentheses. Multiply 5k^2 by each term separately. The result is -30k^4 - 10k^3 + 30k^2. So the simplified expression is -30k^4 - 10k^3 + 30k^2.
20. To simplify the expression (3k+2)(k-3), you can use the distributive property. Multiply each term in the first parentheses by each term in the second parentheses. This gives you 3k^2 - 9k + 2k - 6. Combine like terms, and you get 3k^2 - 7k - 6. So the simplified expression is 3k^2 - 7k - 6.
21. To simplify the expression (-3y+2)(y+3), you can again use the distributive property. Multiply each term in the first parentheses by each term in the second parentheses. This gives you -3y^2 - 9y + 2y + 6. Combine like terms, and you get -3y^2 - 7y + 6. So the simplified expression is -3y^2 - 7y + 6.
I hope this helps! Let me know if you have any other questions.