What should be added to 4c (-a + b + c) to obtain 3a (a + b + c) - 2b (a - b + c)?
Solution:
Let the term to be added be ‘x’
∴ 4c (-a + b + c) + x = 3a (a + b + c) - 2b (a - b + c)
x = 3a (a + b + c) - 2b (a - b + c) - 4c (- a + b + c)
= 3a² + 3ab + 3ac - 2ab + 2b² - 2bc + 4ac - 4bc - 4c²
= 3a² + 2b² - 4c² + 3ab - 2ab - 2bc - 4bc + 3ac + 4ac
= 3a² + 2b² - 4c² +ab - 6bc + 7ac
✦ Try This: What should be added to 5z (-2x + 3y + 7z) to obtain 4x (x + 2y + 3z) - 3y (x - y + 2z)?
Let the term to be added be ‘p’
∴ 5z (-2x + 3y + 7z) + p = 4x (x + 2y + 3z) - 3y (x - y + 2z)
⇒ 5z (-2x + 3y + 7z) + p = 4x² + 8xy + 12xz - 3xy + 3y² - 6yz
⇒ - 10xz + 15yz + 35z² + p = 4x² + 8xy + 12xz - 3xy + 3y² - 6yz
⇒ p = (4x² + 8xy + 12xz - 3xy + 3y² - 6yz) - (- 10xz + 15yz + 35z² )
⇒ p = 4x² + 3y² - 35z² + 5xy - 21yz + 22xz
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9
NCERT Exemplar Class 8 Maths Chapter 7 Problem 115
What should be added to 4c (-a + b + c) to obtain 3a (a + b + c) - 2b (a - b + c)?
Summary:
3a² + 2b² - 4c² +ab - 6bc + 7ac should be added to 4c (- a + b + c) to obtain 3a (a + b + c) - 2b (a - b + c)
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