Question

допоможіть будь ласка дам 30 балов​

Answer 1

1 задание

${( {y}^{4} )}^{3} = {y}^{4 \times 3} = {y}^{12}$

${( { - x}^{6} )}^{2} = - {x}^{6 \times 2} = { x}^{12}$

${m}^{5} {m}^{4} = {m}^{5 + 4} = {m}^{9}$

${( {m}^{5} )}^{4} = {m}^{5 \times 4} = {m}^{20}$

${( {( {a}^{7} )}^{3} )}^{2} = {( {a}^{7 \times 3} )}^{2} = {a}^{21 \times 2} = {a}^{42}$

${( {a}^{6} )}^{3} \times {( {a}^{2} )}^{4} = {a}^{6 \times 3} \times {a}^{2 \times 4} = {a}^{18 + 8} = {a}^{26}$

${a}^{32} \div {( {a}^{9} )}^{3} \times a = {a}^{32} \div {a}^{9 \times 3} \times {a}^{1} = {a}^{32} \div {a}^{27} \times {a}^{1} = {a}^{32 - 27} \times {a}^{1} = {a}^{5} \times {a}^{1} = {a}^{5 + 1} = {a}^{6}$

2 задание

$(x + 2)(x - 5) - 3x(1 - 2x) = {x}^{2} - 5x + 2x - 10 - 3x + 6 {x}^{2} = 7 {x}^{2} - 6x - 10$

$(a + 3)(a - 2) + (a - 3)(a + 6) = {a}^{2} - 2a + 3a - 6 + {a}^{2} + 6a - 3a - 18 = 2 {a}^{2} + 4a - 24$

$(x - 7)(3x - 2) - (5x + 1)(2x - 4) = 3 {x}^{2} - 2x - 21x + 14 - 1 0{x}^{2} + 20x - 2x + 4 = - 7 {x}^{2} - 5x + 18$

$(5x - 2y)(3x + 5y) - (2.5x - 3y)(4x + 8y) = 15 {x}^{2} + 25xy - 6xy - 10 {y}^{2} - 10 {x}^{2} - 20xy + 12xy + 24 {y}^{2} = 5 {x}^{2} + 11xy + 14 {y}^{2}$

$(3 {a}^{2} + 5y)(2 {a}^{3} + y) - 7 {a}^{3} ( {a}^{2} - 3y) = 6 {a}^{5} + 3 {a}^{2} y + 10 {a}^{3} y + 5 {y}^{2} - 7 {a}^{5} + 21 {a}^{3} y = - {a}^{5} + 31 {a}^{3} y + 3 {a}^{2} y + 5 {y}^{2}$

3 задание

$(5x - 3y)(5x + 3y) + (3x - 5y)(3x + 5y) = {(5x)}^{2} + {(3y)}^{2} + {(3x)}^{2} + {(5y)}^{2} = 25 {x}^{2} + 9 {y}^{2} + 9 {x}^{2} + 25 {y}^{2} = 34 {x}^{2} + 34 {y}^{2}$

${(x - 2)}^{2} + (x - 1)(x + 1) = {x}^{2} - 4x + 4 + {x}^{2} + 1 = 2 {x}^{2} - 4x + 5$

$(3a - 2b)(3a + 2b) - {(a + 3b)}^{2} = {(3a)}^{2} + {(2b)}^{2} - {a}^{2} - 6ab - 9 {b}^{2} = 9 {a}^{2} + 4 {b}^{2} - {a}^{2} - 6ab - 9 {b}^{2} = 8 {a}^{2} - 6ab - 5 {b}^{2}$

$(y - 4)(y + 3) + {(y + 1)}^{2} - (7 - y)(7 + y) = {y}^{2} + 3y - 4y - 12 + {y}^{2} + 2y + 1 - 14 - {y}^{2} = {y}^{2} + y - 25$

4 задание

$6a - 9b = 3(2a - 3b)$

$4x - xy = x(4 - y)$

$5ab - 5ac = 5a(b - c)$

$3 {m}^{2} - 6mn = 3m(m - 2n)$

${a}^{7} + {a}^{4} = {a}^{4} ( {a}^{3} + 1)$

$15a {b}^{2} - 5ab = 5ab(3b - 1)$

$24 {x}^{2} y + 36x {y}^{2} = 12xy(2x + 3y)$

$- 4 {x}^{8} + 18 {x}^{15} = - 2 {x}^{8} (2 - 9 {x}^{7} )$

$3 {x}^{4} - 6 {x}^{3} + 9 {x}^{5} = 3 {x}^{3} (x - 2 + 3 {x}^{2} )$