Question

Write the expression in standard form : 2(15y - 9 + 5y^2) + (10 - 6y) - 5y + 9y + 1

a) 5y^2 + 20y + 3
b) 5y^2 + 18y - 7
c) 5y^2 + 18y + 3
d) 5y^2 + 20y - 7

Answer 1

After distributing and combining like terms, the expression in standard form is 10y^2 + 28y - 8, which does not match any of the provided options. There may be a mistake in the answer choices given.

Step-by-step explanation:

To write the expression in standard form, we need to perform the distributive property and then combine like terms. Starting with 2(15y - 9 + 5y2) + (10 - 6y), distribute the 2 into the first parentheses and simplify:

1. 2 × 15y = 30y
2. 2 × -9 = -18
3. 2 × 5y2 = 10y2

This results in 10y2 + 30y - 18.

We then simplify the rest of the expression by combining like terms:

• 10y2 + 30y - 18 + 10 - 6y - 5y + 9y

Combine the y terms (30y - 6y - 5y + 9y) and the constants (-18 + 10):

• 30y - 6y - 5y + 9y = 28y
• -18 + 10 = -8

Now, we can write the expression in standard form:

10y2 + 28y - 8

Finally, let's match our result with one of the given options. None of the options provided match our result, which suggests there may have been a typo or calculation error in the original options given.