Question

(4x^3+5)^2+(4x^3-1)^2-2(4x^3+5)(4x^3-1) ​

Answer 1

16х⁶+40х³+25+63²-32х⁶+8х³-40х³+10= 16х⁶+25+3969-32х⁶+8х³+10=-16х⁶+4004+8х³=-16х⁶+8х³+4004

Answer 2

To simplify the given expression $(4x^3+5)^2+(4x^3-1)^2-2(4x^3+5)(4x^3-1)$, you can follow these steps:

1. Expand the square of each binomial: $(4x^3+5)^2 = (4x^3+5)(4x^3+5) = 16x^6 + 40x^3 + 25$

$(4x^3-1)^2 = (4x^3-1)(4x^3-1) = 16x^6 - 8x^3 + 1$

2. Multiply $2(4x^3+5)(4x^3-1)$: $2(4x^3+5)(4x^3-1) = 2(16x^6 - x^3 - 20x^3 + 5) = 2(16x^6 - 21x^3 + 5)$

3. Now, substitute these expanded expressions back into the original expression and simplify:

$$\begin{align*} &(16x^6 + 40x^3 + 25) + (16x^6 - 8x^3 + 1) - 2(16x^6 - 21x^3 + 5)\\ &= 16x^6 + 40x^3 + 25 + 16x^6 - 8x^3 + 1 - 32x^6 + 42x^3 - 10\\ &= (16x^6 + 16x^6 - 32x^6) + (40x^3 - 8x^3 + 42x^3) + (25 + 1 - 10)\\ &= 0x^6 + 74x^3 + 16\\ &= 74x^3 + 16 \end{align*}$$

So, the simplified form of the expression is $74x^3 + 16$.