Question

Розкладіть вираз на множники і обчисліть його значення при
m = 1/2, n = - 3.5

1) 4mn + 8m - 7n -14:

2) 2m - 32m ^ 3

Answer 1

1)

$4mn+8m-7n-14=4m(n+2)-7(n+2)=(n+2)(4m-7);m=\dfrac{1}{2} ,n=-3,5\\\\(-3,5+2) (4\times\dfrac{1}{2}-7)=-1,5\times(-5)=7,5$

2)

$2m - 32m ^ 3=2m(1-16m^2)=2m(1-4m)(1+4m);m=\dfrac{1}{2} \\\\2\times\dfrac{1}{2}(1-4\times\dfrac{1}{2})(1+4\times\dfrac{1}{2})=1\times(-1)\times3=-3$

Answer 2

1) 4mn + 8m - 7n - 14 = 4m(n+2) -7(n+2) = (n+2)(4m-7) = (-3,5 + 2)(4× 1/2 - 7) = -1,5 × (2-7) = - 1,5×(-5) = 7,5

2) 2m - 32m³ = 2m( 1 - 16m²) = 2m( 1² - (4m)² ) = 2m(1-4m)(1+4m) = 2×1/2 × (1 - 4×1/2)(1 + 4×1/2) = (1 - 2)(1 + 2) = -1 × 3 = -3