Question

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Answer 1

34.4
$\frac{16}{49} p^2q - q^3 = q* ( (\frac{4}{7}p)^2 - q^2) = q( \frac{4}{7}p -q)( \frac{4}{7} p +q) \\ \\ \\ 2 \frac{7}{9} a^3b - \frac{ab^3}{4} = \frac{25}{9} a^3b - \frac{1}{4} ab^3= ab(( \frac{5}{3}a)^2 - (\frac{1}{2} b)^2 ) = \\ \\ =ab(1 \frac{2}{3} a- \frac{1}{2} b)(1 \frac{2}{3} a+\frac{1}{2} b) =ab(1 \frac{2}{3} a- 0.5b)(1 \frac{2}{3} a+0.5b)$
$c^3 - \frac{25}{36} cd^2 = c (c^2 - ( \frac{5}{6} d)^2 ) = c(c - \frac{5}{6} d)(c^2 + \frac{5}{6} d) \\ \\ \\ \frac{mn^5}{9} - 3 \frac{1}{16} m^3n = \frac{1}{9} *mn^5 - \frac{49}{9} m^3n = mn( \frac{1}{9} n^4 - \frac{49}{9} m^2) = \\ \\ =mn( ( \frac{1}{3} n^2)^2 - ( \frac{7}{3} m)^2 ) = mn( \frac{1}{3}n^2 - 2 \frac{1}{3}m)( \frac{1}{3}n^2 +2 \frac{1}{3}m)$


34.5
5a²+10ab +5b² = 5(a²+2ab+b²)= 5(a+b)²= 5(a+b)(a+b)

2x²+4x+2 = 2(x²+2x+1) = 2(x+1)²= 2(x+1)(x+1)

3m²+3n²-6mn = 3(m² +n² -2mn) = 3(m² -2mn+n²)=
=3(m-n)²=3(m-n)(m-n)

8n² - 16n + 8 = 8(n² - 2n +1) = 8(n-1)² = 8(n-1)(n-1)

34.6
-3x²+12x-12= -3(x² -4x +4) = -3(x² -2*x*2+2²) = -3(x-2)²=-3(x-2)(x-2)

-2a³+20a²b -50ab²= -2a(a² -10ab+ 25b²) = -2a(a²-2*a*5b +(5b)²)=
=-2a(a-5b)² = -2a(a-5b)(a-5b)

-5p²-10pq -5q²= -5(p²+10pq+q²) = -5(p+q)²= -5(p+q)(p+q)

-36z³-24z²-4z = -4z(9z² + 6z +1)= -4z( (3a)² +2*3a*1 +1²)=
= -4z(3a+1)² = -4z(3a+1)(3a+1)