Question

1)(2x-1)(4x+2x+1)-4x(2x²-3)при x=0.52)x(x+2)(x-2)-(x-3)(x²+3x+9)при х=1/4​

Answer 1

$\displaystyle \tt 1) \: (2x-1)(4x+2x+1)-4x(2x^2-3)=(2x-1)(6x+1)-8x^3+12x=12x^2+2x-6x-1-8x^3+12x=12x^2+8x-1-8x^3=\bold{-8x^3+12x^2+8x-1}$

$\displaystyle \tt -8\cdot0,5^3+12\cdot0,5^2+8\cdot0,5-1=-1+3+4-1=5$

$\displaystyle \tt 2) \: x(x+2)(x-2)-(x-3)(x^2+3x+9)=x(x^2-4)-(x^3-27)=x^3-4x-x^3+27=\bold{-4x+27}$

$\displaystyle \tt -4\cdot\frac{1}{4}+27=-1+27=26$

Answer 2

1. Let's evaluate the expression (2x-1)(4x+2x+1)-4x(2x²-3) when x = 0.5.

Substituting x = 0.5 into the expression, we have:

(2(0.5) - 1)(4(0.5) + 2(0.5) + 1) - 4(0.5)(2(0.5)² - 3)

Simplifying each part of the expression:

(1 - 1)(2 + 1) - 2(0.5)(2(0.5)² - 3) 0(3) - 2(0.5)(2(0.5)² - 3) 0 - 2(0.5)(2(0.25) - 3) 0 - 2(0.5)(0.5 - 3) 0 - 2(0.5)(-2.5) 0 - 2(-1.25) 0 + 2.5 2.5

Therefore, when x = 0.5, the expression (2x-1)(4x+2x+1)-4x(2x²-3) evaluates to 2.5.

2. Now let's evaluate the expression x(x+2)(x-2)-(x-3)(x²+3x+9) when x = 1/4.

Substituting x = 1/4 into the expression, we have:

(1/4)((1/4) + 2)((1/4) - 2) - ((1/4) - 3)((1/4)² + 3(1/4) + 9)

Simplifying each part of the expression:

(1/4)((1/4 + 8/4)((1/4) - 2) - ((1/4) - 3)((1/4)² + 3(1/4) + 9) (1/4)(9/4)(-7/4) - (-11/4)((1/16) + 3/4 + 9)

Calculating the values:

(9/16)(-7/4) - (-11/4)((1/16) + 3/4 + 9) -63/64 * (-7/4) - (-11/4)(145/16)

Multiplying fractions:

63/256 - 1595/64

To subtract fractions, we need a common denominator:

(63/256)(16/16) - (1595/64)(4/4) 1008/4096 - 6380/256

Now subtracting the fractions:

(1008 - 6380)/4096 -5372/4096

Simplifying the fraction:

-5372 divided by 4 = -1343 4096 divided by 4 = 1024

Therefore, when x = 1/4, the expression x(x+2)(x-2)-(x-3)(x²+3x+9) evaluates to -1343/1024, which is approximately -1.31.