Question

1) (a²+b³)² 2) (¼x-½y)² 3) m²-a²

Answer 1

1) (a²+b³)²  = а⁴+2а²в³+в⁶

2) (¼x-½y)² = 1/16х²-1/4ху+1/4у²

3) m²-a²=(m-a)(m+a)

Answer 2

Sure! Let's simplify the given expressions:

1. (a²+b³)²:

To simplify this expression, we need to expand the square of the binomial (a²+b³):

(a²+b³)² = (a²+b³) * (a²+b³)

Using the FOIL method (First, Outer, Inner, Last), we can expand the expression:

(a²+b³) * (a²+b³) = a² * a² + a² * b³ + b³ * a² + b³ * b³

Simplifying further:

a^4 + a²b³ + a²b³ + b^6 = a^4 + 2a²b³ + b^6

Therefore, (a²+b³)² simplifies to a^4 + 2a²b³ + b^6.

2. (¼x-½y)²:

Similar to the previous expression, we need to expand the square of the binomial (¼x-½y):

(¼x-½y)² = (¼x-½y) * (¼x-½y)

Using the FOIL method:

(¼x-½y) * (¼x-½y) = (¼x) * (¼x) + (¼x) * (-½y) + (-½y) * (¼x) + (-½y) * (-½y)

Simplifying further:

(1/16)x² - (1/8)xy - (1/8)xy + (1/4)y² = (1/16)x² - (1/4)xy + (1/4)y²

Therefore, (¼x-½y)² simplifies to (1/16)x² - (1/4)xy + (1/4)y².

3. m²-a²:

This expression is already in its simplest form and cannot be further simplified.

Therefore, m²-a² remains as m²-a².