Question

A)4a³×(-5a²)²=? b)(2x-3y)²-(3x-y)(3x+y)=?

Answer 1

4a³×(-5a²)²= 4a³×(5a²)²=4a³*24a^4=100a^7

(2x-3y)²-(3x-y)(3x+y)= 4x²-12xy+9y²-(9x²-y²)=4x²-12xy+9y²-9x²+y²=-5x²-12xy+10y²

Answer 2

Let's solve these two expressions step by step:

a) 4a³ × (-5a²)²

First, we'll calculate the square of -5a²:

(-5a²)² = (-5)² * (a²)² = 25 * a^4

Now, multiply 4a³ by 25a⁴:

4a³ * 25a⁴ = 100a^(3+4) = 100a^7

So, the simplified expression is 100a^7.

b) (2x - 3y)² - (3x - y)(3x + y)

First, we'll square the binomial (2x - 3y):

(2x - 3y)² = (2x - 3y)(2x - 3y) = 4x² - 6xy - 6xy + 9y² = 4x² - 12xy + 9y²

Now, expand the product of the two binomials (3x - y)(3x + y) using the difference of squares formula (a² - b² = (a + b)(a - b)):

(3x - y)(3x + y) = (3x)² - (y)² = 9x² - y²

Now, subtract the result of (3x - y)(3x + y) from the squared binomial:

4x² - 12xy + 9y² - (9x² - y²)

Distribute the negative sign inside the parentheses:

4x² - 12xy + 9y² - 9x² + y²

Now, combine like terms:

(4x² - 9x²) + (-12xy) + (9y² + y²) = -5x² - 12xy + 10y²

So, the simplified expression is -5x² - 12xy + 10y².