ГДЗ до підручника «Алгебра» О.С. Істера. 7 клас

§ 11. Множення многочлена на многочлен

339. 1) (x + у)(m + р) = хm + хр + уm + ур;

2) (с - 2)(b + 1) = bс + с - 2b - 2;

3) (3 - t)(a - b) = 3а - 3b - ta + tb;

4) (1 - р)(2 - а) = 2 - a - 2р + ар.

340. 1) (а - b)(х + у) = aх + ay - bx - by;

2) (c + d)(m + n) = cm + cn + dm + dn;

3) (c - a) (m - y) = mc - су - am + ay;

4) (a + 5)(b - 2) = ab - 2a + 5b - 10.

341. 1) (c - 8)(d + 1) = cd + c - 8d - 8;

2) (m + n)(a + b) = ma + mb + na + nb;

3) (a + 2)(x - 3) = ax - 3a + 2x - 6;

4) (m - p)(a - d) = ma - md - ap + pd.

342. 1) (a + 3)(a + 2) = a² + 2a + 3a + 6 = a² + 5a + 6;

2) (y - 2)(p + 4) = y² + 4y - 2y - 8 = y² + 2y - 8;

3) (2 - p)(p + 1) = 2p + 2 - p² - p = 2 - p² + p;

4) (b - 5)(2b + 1) = 2b² + b - 10b - 5 = 2b² - 9b - 5;

5) (3a - 4)(2a + 1) = 6a² + 3a - 8a - 4 = 6a² - 5a - 4;

6) (5y - 3)(1 - 2y) = 5y - 10y² - 3 + 6у = -10y² + 11y - 3.

343. 1) (y + 2)(p - 3) = y² - 3y + 2y - 6 = y² - y - 6;

2) (a - 3)(a - 2) = a² - 2a - 3a + 6 = a² - 5a + 6;

3) (4 - p)(p + 3) = 4p + 12 - p² - 3p = p + 12 - p²;

4) (5a - 2)(a + 3) = 5a² + 15a - 2a - 6 = 5a² + 13a - 6;

5) (4b - 3)(2b - 1) = 8b² - 4b - 6b + 3 - 8b² - 10b + 3;

6) (7m - 2)(1 + 2m) = 7m + 14m² - 2 - 4m = 3m + 14m² - 2.

344. 1) (2 + 4x)(2y - 1) = 4y - 2 + 8xy - 4z;

2) (x² + a)(x - a²) = x³ - x²a² + ax - a³;

3) (4p - 2m)(3p + 5m) = 12p² + 20mp - 6mp - 10m² = 12p² + 14mp - 10m²;

4) (2x² - 1) (3x + 1) = 6x³ + 2x² - 3x - 1;

5) (7x² - 4x)(3x - 2) = 21x³ - 14x² - 12x² + 8x = 21x³ - 26x² + 8x;

6) (b - 2)(3b³ - 4b²) = 3b⁴ - 4b³ - 6b³ + 8b² = 3b⁴ - 10b³ + 8b²;

7) (m² - 2m)(3m - 7m²) = 3m³ - 7m⁴ - 6m² + 14m³ = 17m³ - 7m⁴ - 6m²;

8) (n³ - 2n²)(n + 7) = n⁴ + 7n³ - 2n³ - 14n² = n⁴ + 5n³ - 14a².

345. 1) (3m² -p)(m² + p) = 3m⁴ + 3m²p - pm² - p² = 3m⁴ + 2m²p - p²;

2) (5a² + b)(b² - 4a²) = 5a²b² - 20a⁴ + b³ - 4a²b;

3) (12a² - 3)(5a - 7a²) = 60a³ - 84a⁴ - 15a + 21a²;

4) (2a³ - 3a²)(a + 5) = 2a⁴ + 10a³ - 8a³ - 15a² - 2a⁴ + 7a³ - 16a².

346. 1) (m - n)(a + b - 1) = ma + mb - m - an - bn + n;

2) (3 - a)(p + 5 - m) = 3p + 15 - 3m - ap - 5a + am;

3) (a + x - 3)(n + 2) = an + 2a + xn + 2x - 3n - 6;

4) (c - d - 7)(x + y) = cx + су – dx - dy - 7x - 7y.

347. 1) (a + b)(m - 2 + p) = am + ap - 2a + bm - 2b + bp;

2) (5 - x)(m - n - p) = 5m - 5n - 5p - mx + xn + xp;

3) (x + у - 2)(a - m) = ax - mx + ay - ym - 2a + 2m;

4) (p + q + 3) (-a - x) = -ap - xp - aq - xq - 3a - 3x.

348. 1) (2x + 7)(2x - 4) + 28 = 4x² - 8x + 14x - 28 + 28 = 4x² + 6x;

2) 5m² + (3 - 5m)(m + 2) = 5m² + 3m + 6 - 5m² - 10m = 6 - 7m;

3) (a + 7)(a - 2) - a(a + 5) = a² - 2a + 7a - 14 - a² - 5a = -14;

4) (2b + 1)(3b - 1) - (6b² - 1) - 6b² - 2b + 3b - 1 - 6b² + 1 = b.

349. 1) (2p - 1)(3p + 5) - 6p² = 6p² + 10р - 3p - 5 - 6p² - 7p - 5;

2) 12 + (3m - 2)(5m + 6) = 12 + 15m² + 18m - 10m - 12 - 15m² + 8m;

3) (m + 3)(m - 5) - m(m - 2) = m² - 5m + 3m - 15 - m² + 2m = -15;

4) (3a - 2)(4a + 1) - (12a² - 2) = 12a² + 3a - 8a - 2 - 12a² + 2 = -5a.

350. 1) (2a - 3)(3a + 5) - 6a² = 6a² + 10a - 9a - 15 - 6a² = a - 15 = 13,5 - 15 = -1,5;

2) (5x - 1)(1 - 2x) -7x = 5x - 10x² - 1 + 2x - 7x = -10x² - 1. Якщо x = -2, то -10 • (-2)² - 1 = -40 - 1 = -41.