Question
upstudy study bank question image url

\( \begin{array}{ll}\text { 816. Преобразуйте выражение в многочлен: }(10-c)^{2} ; & \text { к) }(0,3-m)^{2} \text {. } \\ \begin{array}{ll}\text { д) }(y-9)^{2} ; & \text { д) }(a-25)^{2} \text {; } \\ \text { б) }(c-d)^{2} ; & \text { е) }(40+b)^{2} ; \\ \text { в) }(x+9)^{2} ; & \text { ж) }(0,2-x)^{2} ; \\ \text { г) }(8-a)^{2} ; & \text { з) }(k-0,5)^{2} .\end{array}\end{array} \)

Ask by Olson Burns. in Russia
Mar 20,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Вот раскрытые выражения: 1. \( (10 - c)^2 = 100 - 20c + c^2 \) 2. \( (0.3 - m)^2 = 0.09 - 0.6m + m^2 \) 3. \( (y - 9)^2 = y^2 - 18y + 81 \) 4. \( (a - 25)^2 = a^2 - 50a + 625 \) 5. \( (c - d)^2 = c^2 - 2cd + d^2 \) 6. \( (40 + b)^2 = 1600 + 80b + b^2 \) 7. \( (x + 9)^2 = x^2 + 18x + 81 \) 8. \( (0.2 - x)^2 = 0.04 - 0.4x + x^2 \) 9. \( (8 - a)^2 = 64 - 16a + a^2 \) 10. \( (k - 0.5)^2 = k^2 - k + 0.25 \)

Solution

Simplify the expression by following steps: - step0: Calculate: \(\left(c-d\right)^{2}\) - step1: Calculate: \(c^{2}-2cd+d^{2}\) Expand the expression \( (k-0.5)^{2} \) Simplify the expression by following steps: - step0: Calculate: \(\left(k-0.5\right)^{2}\) - step1: Convert the expressions: \(\left(k-\frac{1}{2}\right)^{2}\) - step2: Calculate: \(k^{2}-k+\frac{1}{4}\) Expand the expression \( (x+9)^{2} \) Simplify the expression by following steps: - step0: Calculate: \(\left(x+9\right)^{2}\) - step1: Calculate: \(x^{2}+18x+81\) Expand the expression \( (40+b)^{2} \) Simplify the expression by following steps: - step0: Calculate: \(\left(40+b\right)^{2}\) - step1: Calculate: \(1600+80b+b^{2}\) Expand the expression \( (0.2-x)^{2} \) Simplify the expression by following steps: - step0: Calculate: \(\left(0.2-x\right)^{2}\) - step1: Convert the expressions: \(\left(\frac{1}{5}-x\right)^{2}\) - step2: Calculate: \(\frac{1}{25}-\frac{2}{5}x+x^{2}\) Expand the expression \( (0.3-m)^{2} \) Simplify the expression by following steps: - step0: Calculate: \(\left(0.3-m\right)^{2}\) - step1: Convert the expressions: \(\left(\frac{3}{10}-m\right)^{2}\) - step2: Calculate: \(\frac{9}{100}-\frac{3}{5}m+m^{2}\) Expand the expression \( (10-c)^{2} \) Simplify the expression by following steps: - step0: Calculate: \(\left(10-c\right)^{2}\) - step1: Calculate: \(100-20c+c^{2}\) Expand the expression \( (y-9)^{2} \) Simplify the expression by following steps: - step0: Calculate: \(\left(y-9\right)^{2}\) - step1: Calculate: \(y^{2}-18y+81\) Expand the expression \( (a-25)^{2} \) Simplify the expression by following steps: - step0: Calculate: \(\left(a-25\right)^{2}\) - step1: Calculate: \(a^{2}-50a+625\) Expand the expression \( (8-a)^{2} \) Simplify the expression by following steps: - step0: Calculate: \(\left(8-a\right)^{2}\) - step1: Calculate: \(64-16a+a^{2}\) Вот преобразованные выражения в многочлены: 1. \( (10-c)^{2} = 100 - 20c + c^{2} \) 2. \( (0.3-m)^{2} = \frac{9}{100} - \frac{3}{5}m + m^{2} \) 3. \( (y-9)^{2} = y^{2} - 18y + 81 \) 4. \( (a-25)^{2} = a^{2} - 50a + 625 \) 5. \( (c-d)^{2} = c^{2} - 2cd + d^{2} \) 6. \( (40+b)^{2} = 1600 + 80b + b^{2} \) 7. \( (x+9)^{2} = x^{2} + 18x + 81 \) 8. \( (0.2-x)^{2} = \frac{1}{25} - \frac{2}{5}x + x^{2} \) 9. \( (8-a)^{2} = 64 - 16a + a^{2} \) 10. \( (k-0.5)^{2} = k^{2} - k + \frac{1}{4} \) Если у вас есть дополнительные вопросы или нужно что-то еще, дайте знать!

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

The Deep Dive

Давайте разложим каждое из приведенных выражений с помощью формулы квадрата разности, которая звучит так: \( (a-b)^2 = a^2 - 2ab + b^2 \). 1. \( (10 - c)^2 = 100 - 20c + c^2 \) 2. \( (0.3 - m)^2 = 0.09 - 0.6m + m^2 \) 3. \( (y - 9)^2 = y^2 - 18y + 81 \) 4. \( (a - 25)^2 = a^2 - 50a + 625 \) 5. \( (c - d)^2 = c^2 - 2cd + d^2 \) 6. \( (40 + b)^2 = 1600 + 80b + b^2 \) 7. \( (x + 9)^2 = x^2 + 18x + 81 \) 8. \( (0.2 - x)^2 = 0.04 - 0.4x + x^2 \) 9. \( (8 - a)^2 = 64 - 16a + a^2 \) 10. \( (k - 0.5)^2 = k^2 - k + 0.25 \) Теперь вы можете увидеть, как из этих выражений получаются многочлены. Это просто!

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy