Subtract the sum of 12ab -10b² -18a² and 9ab + 12b² + 14a² from the sum of ab + 2b² and 3b² - a²
Solution:
We have to subtract the sum of 12ab -10b² -18a² and 9ab + 12b² + 14a² from the sum of ab + 2b² and 3b² - a².
Sum of 12ab -10b² -18a² and 9ab + 12b² + 14a² = 12ab -10b² -18a² + (9ab + 12b² + 14a²)
= 12ab -10b² -18a² + 9ab + 12b² + 14a²
By combining like terms,
= 12ab + 9ab - 10b² + 12b² - 18a² + 14a²
= (12 + 9)ab + (-10 + 12)b² + (-18 + 14)a²
= (21)ab + (2)b² + (-4)a²
= 21ab + 2b² - 4a²
Sum of ab + 2b² and 3b² - a² = ab + 2b² + (3b² - a²)
= ab + 2b² + 3b² - a²
By combining like terms,
= ab + 2b² + 3b² - a²
By distributive property,
= ab + (2 + 3)b² - a²
= ab + 5b² - a²
On subtracting 21ab + 2b² - 4a² from ab + 5b² - a²,
= ab + 5b² - a² - (21ab + 2b² - 4a²)
= ab + 5b² - a² - 21ab - 2b² + 4a²
By combining like terms,
= ab - 21 ab + 5b² - 2b² - a² + 4a²
By distributive property,
= (1 - 21)ab + (5 - 2)b² + (-1 + 4)a²
= (-20)ab + (3)b² + (3)a²
Therefore, the required expression is -20ab + 3b² + 3a².
✦ Try This: Subtract the sum of 20ab -11b² -19a² and 21ab + 13b² + 16a² from the sum of ab + 9b² and 7b² - 4a²
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 12
NCERT Exemplar Class 7 Maths Chapter 10 Problem 71
Subtract the sum of 12ab -10b² -18a² and 9ab + 12b² + 14a² from the sum of ab + 2b² and 3b² - a²
Summary:
On subtracting the sum of 12ab -10b² -18a² and 9ab + 12b² + 14a² from the sum of ab + 2b² and 3b² - a², we get -20ab + 3b² + 3a²
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