Question

(x-4)(x+2(x-7)(x+8)(x-5)(x+7)(x-11)×(x+12)(x-16)(x+14)​

Answer 1

$(x-4)(x+2)=x^2+2x-4x-8=x^2-2x-8\\\\(x-7)(x+8)=x^2+8x-7x-56=x^2+x-56\\\\(x-5)(x+7)=x^2+7x-5x-35=x^2+2x-35\\\\(x-11)(x+12)=x^2+12x-11x-132=x^2+x-132\\\\(x-16)(x+14)=x^2+14x-16x-224=x^2-2x-224$

Answer 2

It looks like you're trying to expand the given expression. To do this, you can use the distributive property to multiply the factors. Let's break it down step by step:

Expression: (x-4)(x+2)(x-7)(x+8)(x-5)(x+7)(x-11)(x+12)(x-16)(x+14)

We'll start by multiplying pairs of factors:

1. (x-4)(x+2) = x(x) + x(2) - 4(x) - 4(2) = x^2 + 2x - 4x - 8 = x^2 - 2x - 8

2. (x-7)(x+8) = x(x) + x(8) - 7(x) - 7(8) = x^2 + 8x - 7x - 56 = x^2 + x - 56

3. (x-5)(x+7) = x(x) + x(7) - 5(x) - 5(7) = x^2 + 7x - 5x - 35 = x^2 + 2x - 35

4. (x-11)(x+12) = x(x) + x(12) - 11(x) - 11(12) = x^2 + 12x - 11x - 132 = x^2 + x - 132

Now, we can continue multiplying the results:

1. (x^2 - 2x - 8)(x^2 + x - 56) = x^2(x^2 + x - 56) - 2x(x^2 + x - 56) - 8(x^2 + x - 56)

Now, distribute within each term:

= x^4 + x^3 - 56x^2 - 2x^3 - 2x^2 + 112x - 8x^2 - 8x + 448

Combine like terms:

= x^4 - x^3 - 66x^2 + 104x + 448

Now, we'll multiply this result by the next factor:

2. (x^4 - x^3 - 66x^2 + 104x + 448)(x^2 - 132)

Now, distribute within each term:

= (x^4)(x^2 - 132) - (x^3)(x^2 - 132) - (66x^2)(x^2 - 132) + (104x)(x^2 - 132) + (448)(x^2 - 132)

= x^6 - 132x^4 - x^5 + 132x^3 - 66x^4 + 8712x^2 + 104x^3 - 132x^2 + 448x^2 - 132*448

Combine like terms:

= x^6 - x^5 - 68x^4 + 104x^3 + 8556x^2 - 132*448

Finally, you can simplify the expression further if needed.