Question

1) (x-3)(х2 +3х +9) -х(х-3)(х+3)+ 27, если х=-10; 2) (x+2)(x2-2x+4)-х(х-4)(х+4)-8, если х = -5.​

Answer 1

1)

(x-3)(х² +3х +9) -х(х-3)(х+3)+ 27=(x-3)·(x²+3x+9-x·(x+3))+27=

=(x-3)·(x²+3x+9-x²-3x)+27=9·(x-3)+27

если x=-10

9·(-10-3)+27=-117+27=-90

2)

(x+2)(x²-2x+4)-х(х-4)(х+4)-8=(x³+8)-x·(x²-16)=x³+8-x³+16x=16x+8

если x=-5

16x+8=16·(-5)+8=-80+8=-72

Answer 2

To evaluate the given expressions for the specified values of x, simply substitute the value of x into the expressions and perform the arithmetic operations. Let's solve each expression step by step:

1. Evaluate (x-3)(x^2 + 3x + 9) - x(x-3)(x+3) + 27 for x = -10:

Step 1: Substitute x = -10 into the first term: (x-3)(x^2 + 3x + 9) (-10 - 3)((-10)^2 + 3*(-10) + 9) (-13)(100 - 30 + 9) (-13)(79) -1027

Step 2: Substitute x = -10 into the second term: -x(x-3)(x+3) -(-10)(-10-3)(-10+3) 10*(-13)(-7) 10*91 910

Step 3: Add the results of Step 1 and Step 2: -1027 + 910 -117

Step 4: Add the last term: -117 + 27 -90

So, the value of the expression when x = -10 is -90.

2. Evaluate (x+2)(x^2 - 2x + 4) - x(x-4)(x+4) - 8 for x = -5:

Step 1: Substitute x = -5 into the first term: (x+2)(x^2 - 2x + 4) (-5 + 2)((-5)^2 - 2*(-5) + 4) (-3)(25 + 10 + 4) (-3)(39) -117

Step 2: Substitute x = -5 into the second term: -x(x-4)(x+4) -(-5)(-5-4)(-5+4) 5*(-9)*(-1) 45

Step 3: Add the results of Step 1 and Step 2: -117 + 45 -72

Step 4: Subtract the last term: -72 - 8 -80

So, the value of the expression when x = -5 is -80.