Question

B^6-(x-4b^3)^2= ? С объяснением.

Answer 1

$b^6-(x-4b^3)^2=(b^3-(x-4b^3))(b^3+(x-4b^3))=(b^3-x+4b^3)(b^3+x-4b^3)=\\ \\ =(5b^3-x)(-3b^3+x)$

Answer 2

To simplify the expression B^6 - (x - 4b^3)^2, we need to expand the squared term and then combine like terms. Let's walk through the process step by step:

Step 1: Expand the squared term. When we square the binomial (x - 4b^3)^2, we get the following result using the FOIL method (First, Outer, Inner, Last):

(x - 4b^3)^2 = (x - 4b^3)(x - 4b^3) = xx - x4b^3 - 4b^3x + 4b^34b^3 = x^2 - 4bx^3 - 4bx^3 + 16b^6 = x^2 - 8bx^3 + 16b^6

Step 2: Substitute the expanded expression back into the original expression. Now, we can replace (x - 4b^3)^2 in B^6 - (x - 4b^3)^2 with its expanded form:

B^6 - (x - 4b^3)^2 = B^6 - (x^2 - 8bx^3 + 16b^6)

Step 3: Combine like terms. The expression contains two terms, B^6 and -(x^2 - 8bx^3 + 16b^6). To simplify, we can distribute the negative sign to each term inside the parentheses:

B^6 - (x^2 - 8bx^3 + 16b^6) = B^6 - x^2 + 8bx^3 - 16b^6

And there you have it! The simplified expression is B^6 - x^2 + 8bx^3 - 16b^6.