1) 12+5√27-√48= 12+15√3-4√3= 12+11√3
2) (√7-√2)(√7+√2)+√56= √7²-√2²+2√14= 7-2+2√14= 5+2√14
3) (2+√5)(√5-2)= √5²-2²= 5-4= 1
4) √8+√2= 2√2+√2= 3√2
5) (√7-1)*(√7-1)= 7-2√7+1= 8-2√7
6) (√5x-√5y)(√5x-√5y)-5(x+y)= 5x-5√xy+5y-5x-5y= -5√xy
7) 6-3√x/4-x= 3(2-√x)/(2-√x)(2+√x)= 3/(2+√x)
1a) ay - 12bx + 3ax - 4by = (ay - 4by) + (3ax - 12bx) = y(a - 4b) + 3x(a - 4b) = (a - 4b)(y + 3x)
1б) x² - 8x + 15 = (x - 5)(x - 3)
2a) (y - 5)² - ( y - 2)5y = y² - 10y + 25 - 5y² + 10y = - 6y² + 25
2б) - 4(p - 2a)² = -4(p² - 4ap + 4a²) = - 4p² + 16ap - 16a²
3a) 16x² + 8xy + y² = (4x + y)²
3б) 49p² - 14p + 1 = (7p - 1)²
4a) (3 - 1/5a)(3 + 1/5a) = 3² - (1/5a)² = 9 - 1/25a² = 9 - 0,04a²
4б) (5b² + 1)(1 - 5b²) = 1² - (5b²)² = 1 - 5b⁴
5a) x²y⁴ - 1 = (xy²)² - 1² = (xy² - 1)(xy² + 1)
5б) 81 - 64x²y² = 9² - (8xy)² = (9 - 8xy)(9 + 8xy)
<span>1.
a</span>) <span>c</span> * <span>c</span>^15 : (<span>c</span>^7)^2= <span>c</span>^16/с^14= <span>c</span>^2
<span> </span><span>б</span><span>) -x^3y^2+ 2x^3y^2 - 3x^3y^2= x^3y^2(-1+2-3)
</span><span>в</span><span>) (2ab^3)^4 : (2a^2b)^2=2ab^12/2a^4b^2=a^-3*b^10
</span><span>г</span><span>)(n^8)^4 * n : (n^3)^11= n^32*n / n^33=n^33/n^33=n
2. 10^9 : (2^3)^3 * (5^3)^2=5^3
1) 10^9:2^9=5^9*2^9/2^9=5^9 (сократим 2^9)
2)5^9:5^6=5^3 (вычтем)
3. <span> (3/4)^8 * (4/3)^7<span> > </span> (-0.75)^0</span>
(3/4)^8*(4/3)^7=3^7*4^6
(-0.75)^0=1
5.<span> (25x^3)^2 * (5x^5)^3 : (125x^8)^2 = 25x^6*5x^15/125x^16=125x^21/125x^16=125x^5
</span>4 напишу позже если решу, в сообщении
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<span>4a3-ab2= a(4a2-b2)=a(2a-b)(2a+b)</span>