Lesson: Expanding Expressions

Comment on Expanding Expressions

Hi Brent.

In another video we could not combine 2^5 + 2^5 to equal 4^10. What we did was have: 2 * 2^5 = 2^6.

I was confused that -3a^2b - 3a^2b = -6a^2b.

Does this also mean that 2^5 + 2^5 = 4^5? That is clearly incorrect but what is the difference going on here?

gmat-admin's picture

You're referring to the expansion I perform at 5:45 in the above video.

It all comes down to the difference between the BASES (of powers) and COEFFICIENTS.

If we are adding powers, we cannot combine bases.
For example, 3² + 3² does not equal 6²
Likewise, x³ + x³ does not equal (2x)³

We can, however, combine the coefficients.
For example 5x³ + 3x³ = 8x³

IMPORTANT: With the term 5x³, we are not cubing 5x.
That is 5x³ does NOT equal (5x)³
Rather 5x³ = (5)(x³)

In other words, 5x³ = x³ + x³ + x³ + x³ + x³
Likewise, 2x³ = x³ + x³
So, 5x³ + 2x³ = (x³ + x³ + x³ + x³ + x³) + (x³ + x³) = 7x³

It's also important to point out that in the expression 3a^2b, the base is a, and the coefficient is 3.
That is, the base is NOT 3a.
If we wanted to say that the base is 3a, we'd write (3a)^2b

Since the coefficient is 3, we can write: 3a^2b = (3)(a^2b) = (a^2b) + (a^2b) + (a^2b)

So, 3a^2b + 3a^2b = (3)(a^2b) + (3)(a^2b)
= (a^2b) + (a^2b) + (a^2b) + (a^2b) + (a^2b) + (a^2b)
= 6(a^2b)
= 6a^2b

Likewise, -3a^2b - 3a^2b = -6a^2b

Does that help?

Here's the video that explains coefficients: https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...

Here's the video on simplifying expressions: https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...

Cheers,
Brent

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