Question

33.2. 1) (4x + 1)³; 5) (a + 2x)³; 33.3. 1) (0,2a + 5)³. 2) (1 - 3y)³; 6) (2y - 3)³; 7)(z-t)³; 3) (5z - 2)³; 7) (p - 3q)³; 8) (k+ m). 4) (4x - 3)³; 8) (3n-2m)³.​

Answer 1

Ответ:

1) (4х+1)³= (4х)³+3×(4х)²×1+3×4х×1²+1³= 64х³+48х²+12х+1.

5) (а+2х)³= а³+3×а²×2х+3×а×(2х)²+(2х)³=а³+6а²х+12ах²+8х³.

1) (0,2а+5)³=(0,2а)³+3×(0,2а)²×5+3×0,2а×5²+5³= 0,008а³+0,6а²+3а+125.

2) (1-3у)³= 1³-3×1²×3у+3×1×(3у)²-(3у)³=1-9у+27у²-27у³.

6) (2у-3)³= (2у)³-3×(2у)²×3+3×2у×3²-3³=8у³-36у²+54у-27.

7) (z-t)³= z³-3z²t+3zt²-t³

3) (5z-2)³= (5z)³-3×(5z)²×2+3×5z×2²-2³=125z³-150z²+60z-8.

7) (p-3q)³=p³-3×p²×3q+3×p×(3q)²-(3p)³=p³-9p²q+ 27pq²-27q³.

8) (k+m)= k³+3k²m+3km²+m³.

4) (4x-3)³= (4x)³-3×(4x)²×3+3×4x×3²-3³=64x³-144x²+108x-27.

8) (3n-2m)³= (3n)³-3×(3n)²×2m+3×3n×(2m)²-(2m)³=27n³-54n²m+36nm²-8m³.

Answer 2

It looks like you've provided several expressions in the form of (a ± b)³, and you'd like to expand them. To expand these expressions, you can use the binomial expansion formula, which is commonly known as the "cube of a binomial." The formula for expanding (a ± b)³ is:

(a ± b)³ = a³ ± 3a²b ± 3ab² ± b³

Now, let's apply this formula to the expressions you provided:

1. (4x + 1)³: (4x + 1)³ = (4x)³ + 3(4x)²(1) + 3(4x)(1²) + 1³ = 64x³ + 48x² + 12x + 1

2. (a + 2x)³: (a + 2x)³ = (a)³ + 3(a)²(2x) + 3(a)(2x)² + (2x)³ = a³ + 6a²x + 12ax² + 8x³

3. (0,2a + 5)³: (0,2a + 5)³ = (0,2a)³ + 3(0,2a)²(5) + 3(0,2a)(5²) + 5³ = 0 + 0 + 0 + 125 = 125

4. (1 - 3y)³: (1 - 3y)³ = (1)³ - 3(1)²(3y) + 3(1)(3y)² - (3y)³ = 1 - 9y + 27y² - 27y³

5. (2y - 3)³: (2y - 3)³ = (2y)³ - 3(2y)²(3) + 3(2y)(3²) - 3³ = 8y³ - 36y² + 54y - 27

6. (z - t)³: (z - t)³ = (z)³ - 3(z)²(t) + 3(z)(t²) - (t)³ = z³ - 3z²t + 3zt² - t³

7. (5z - 2)³: (5z - 2)³ = (5z)³ - 3(5z)²(2) + 3(5z)(2²) - (2)³ = 125z³ - 150z² + 60z - 8

8. (p - 3q)³: (p - 3q)³ = (p)³ - 3(p)²(3q) + 3(p)(3q)² - (3q)³ = p³ - 9p²q + 27pq² - 27q³

9. (k + m)³: (k + m)³ = (k)³ + 3(k)²(m) + 3(k)(m²) + (m)³ = k³ + 3k²m + 3km² + m³

10. (3n - 2m)³: (3n - 2m)³ = (3n)³ - 3(3n)²(2m) + 3(3n)(2m)² - (2m)³ = 27n³ - 54n²m + 36nm² - 8m³

These are the expanded forms of the expressions you provided.