Question

1)Запишите произведение в виде многочлена: а) (-4pq + 7p²r) * 3q³r б)12x²yz(2x²z - y² - 3yz³). 2)Упростите выражение 3m³n(n - 2n²) - (3m² - n - 6m²n) и найдите его значение при m = 5 , n = -2

Answer 1

№1
а) (-4pq + 7p²r)·3q³r = -12pq^4r + 21p²q³r²
б) = 24x^4yz² - 12 x²y³z - 36x²y²z^4
№2
= 3m³n² - 6 m³n³ - 3 m² +n +6m²n=
=3·5³·(-2)² - 6·5³·(-2)³ - 3·5²-2+6·5²·(-2) =
=3·125·4 + 6·125·8 -3·25 -2 - 6·25·2=
=1500+6000 - 75 -2 -300 = 7500 = 377 = 7123

Answer 2

1) Запишите произведение в виде многочлена:

а) (-4pq + 7p²r) * 3q³r

To multiply these polynomials, we can use the distributive property. We'll multiply each term of the first polynomial by each term of the second polynomial and then combine like terms.

Multiplying the first terms: (-4pq) * (3q³r) = -12p*q*q³*r = -12pq⁴r

Multiplying the second terms: (-4pq) * (3q³r) = 7p²r * (3q³r) = 21p²q³r²

Combining the terms, we get: (-12pq⁴r) + (21p²q³r²)

So, the product of (-4pq + 7p²r) and (3q³r) is -12pq⁴r + 21p²q³r².

б) 12x²yz(2x²z - y² - 3yz³)

To multiply these polynomials, we'll use the distributive property again. We'll multiply each term of the first polynomial by each term of the second polynomial and then combine like terms.

Multiplying the first terms: 12x²yz * 2x²z = 24x⁴yz²

Multiplying the second terms: 12x²yz * -y² = -12x²y³z

Multiplying the third terms: 12x²yz * -3yz³ = -36x²y²z⁴

Combining the terms, we get: 24x⁴yz² - 12x²y³z - 36x²y²z⁴

So, the product of 12x²yz and (2x²z - y² - 3yz³) is 24x⁴yz² - 12x²y³z - 36x²y²z⁴.

2) Упростите выражение 3m³n(n + 2n²) - (3m² - n - 6m²n) и найдите его значение при m = 5, n = -2

To simplify the expression, let's simplify each term and then combine like terms.

Term 1: 3m³n(n + 2n²) = 3m³n * n + 3m³n * 2n² = 3m³n² + 6m³n³

Term 2: -(3m² - n - 6m²n) = -3m² + n + 6m²n

Now, let's combine the terms: 3m³n² + 6m³n³ - 3m² + n + 6m²n

To find the value of this expression when m = 5 and n = -2, we substitute these values into the expression: 3(5³)(-2)² + 6(5³)(-2)³ - 3(5²) + (-2) + 6(5²)(-2)

Calculating this expression, we get: 3(125)(4) + 6(125)(-8) - 3(25) - 2 + 6(25)(-2) = 1500 - 6000 - 75 - 2 - 300 = -6277

So, the value of the expression 3m³n(n + 2n²) - (3m² - n - 6m²n) when m = 5 and n = -2 is -6277.