<span>1.</span>
<span>а)x^3-2x = х(х²-2)</span>
<span><span>б)5a^2-10ab+5b^2 = 5(<span>a^2-2ab+b^2</span>) = 5(a-b)²</span></span>
<span><span><span>в)cm-cn+3m-3n = (<span>cm-cn)+(3m-3n) = с(m-n)+3(m-n) = (с+3)(m-n)</span></span></span></span>
<span><span><span><span>2.</span></span></span></span>
<span><span><span><span><span>2(p+q)²-p(4q-p)+q² = <span>3p²+3q² при любых p и q</span></span></span></span></span></span>
<span><span><span><span><span><span>2(p+q)²-p(4q-p)+q² = 2(p²+2pq+q²) -4pq+p²+q² = 2p²+4pq+2q² -4pq+p²+q² = 3p²+3q² </span></span></span></span></span></span>
<span><span><span><span><span><span>таким образом, мы привели левую часть к правой, тем самым доказав, что значения выражений будут равны при любых p и q</span></span></span></span></span></span>
<span><span><span><span><span><span>3.</span></span></span></span></span></span>
<span><span><span><span><span><span><span>(x-3)(x+3) = x(x-2)</span></span></span></span></span></span></span>
<span><span><span><span><span><span><span>х²-9=х²-2х</span></span></span></span></span></span></span>
<span><span><span><span><span><span><span>2х=9</span></span></span></span></span></span></span>
<span><span><span><span><span><span><span>х=4,5</span></span></span></span></span></span></span>
<span><span><span><span><span><span><span>Ответ: при х=4,5 </span></span></span></span></span></span></span>
<span><span><span><span><span><span><span>4.</span></span></span></span></span></span></span>
<span><span><span><span><span><span><span><span>а)(a-3b)(a+3b)+(2b+a)(a-2b) = (a²-9b²) + (a²-4b²) = 2a²-13b²</span></span></span></span></span></span></span></span>
<span><span><span><span><span><span><span><span><span>б)(p+q)(q-p)(q²+p²) = (q²-p²)(q²+p²) = q⁴-p⁴</span></span></span></span></span></span></span></span></span>
<span><span><span><span><span><span><span><span><span>5.</span></span></span></span></span></span></span></span></span>
<span><span><span><span><span><span><span><span><span><span>x³-27-3x(x-3)=0</span></span></span></span></span></span></span></span></span></span>
(x³-3³)-3x(x-3)=0
воспользуемся формулой разности кубов:
(х-3)(х²+3х+9)-3x(x-3)=0
(х-3)(х²+3х+9-3х)=0
х-3=0 или (х²+3х+9-3х)=0
х=3 х²+9=0
х²=-9 - решений нет
Ответ: х=3