Question

Are the expressions 8a2 - 4b + 7a2 and 5(3a2 - 2b) + 6b equivalent? Explain your reasoning.

Answer 1

Answer:

Yes, The expressions 8a² - 4b + 7a² and 5(3a² - 2b) + 6b are equivalent

Step-by-step explanation:

To answer the question you must simplify each expression, then compare them to find if they are equivalent or not  

∵ The 1st expression = 8a² - 4b + 7a²  

→ Add the like terms

∴ The 1st expression = (8a² + 7a²) - 4b

∴ The 1st expression = 15a² - 4b

∵ The 2nd expression = 5(3a² - 2b) + 6b

→ Multiply the bracket by 5

∴ The 2nd expression = 5(3a²) - 5(2b) + 6b

∴ The 2nd expression = 15a² - 10b + 6b

→ Add the like terms

∵ The 2nd expression = 15a² + (-10b + 6b)

∴ The 2nd expression = 15a² + -4b

→ Remember (+)(-) = (-)

∴ The 2nd expression = 15a² - 4b

∵ The 1st expression = The 2nd expression

∴ The two expressions are equivalent

∴ The expressions 8a² - 4b + 7a² and 5(3a² - 2b) + 6b are equivalent