simplify the following expression without using calculator.
-2(-4a squared + b cube) square
........
-2 (-4a squared + b cube)(-4a squared + b cube)
-2 (16a square - 4a square b cube + b cube)
-2 (+ 16 a square = b cube )
-32a square - 2b cube.
please retype
we use x^2 for x squared, x^3 for x cubed etc
What does ..... mean ?
If you mean division, then use / for the division sign and place brackets in the correct positions
To simplify the expression -2(-4a^2 + b^3)^2, start by expanding the squared term inside the parentheses:
(-4a^2 + b^3)^2 = (-4a^2 + b^3)(-4a^2 + b^3)
To simplify this, use the distributive property and FOIL method.
(-4a^2 + b^3)(-4a^2 + b^3) = -4a^2*(-4a^2) + (-4a^2)*(b^3) + (b^3)*(-4a^2) + (b^3)*(b^3)
Simplifying further:
= 16a^4 - 4a^2b^3 - 4a^2b^3 + b^6
Combine like terms:
= 16a^4 - 8a^2b^3 + b^6
Finally, multiply the simplified expression by -2:
-2(16a^4 - 8a^2b^3 + b^6) = -32a^4 + 16a^2b^3 - 2b^6
Therefore, the simplified expression is -32a^4 + 16a^2b^3 - 2b^6.
To simplify the expression -2(-4a^2 + b^3)^2, you follow the order of operations, which includes working with exponents and applying the distributive property. Here's the step-by-step process:
Step 1: Square the expression inside the parentheses.
(-4a^2 + b^3)^2 = (-4a^2 + b^3)(-4a^2 + b^3)
Step 2: Apply the distributive property by multiplying each term in the first parentheses with each term in the second parentheses.
(-4a^2 + b^3)(-4a^2 + b^3) = -4a^2 * -4a^2 + -4a^2 * b^3 + b^3 * -4a^2 + b^3 * b^3
Step 3: Simplify each multiplication.
16a^4 - 4a^2b^3 - 4a^2b^3 + b^6
Step 4: Combine like terms.
16a^4 - 8a^2b^3 + b^6
Finally, we can multiply the entire expression by -2 to get the simplified form:
-2(16a^4 - 8a^2b^3 + b^6) = -32a^4 + 16a^2b^3 - 2b^6
Therefore, the simplified expression is -32a^4 + 16a^2b^3 - 2b^6.