Développer, Réduire et Factoriser

a) $10 - (a + 5) = 10 - a - 5 = $ $-a + 5$

b) $3x + (4x - 2) = 3x + 4x - 2 = $ $7x - 2$

c) $7y - (2y - 8) = 7y - 2y + 8 = $ $5y + 8$

d) $-(b + 3) + (2b - 1) = -b - 3 + 2b - 1 = $ $b - 4$

e) $5 - (x^2 - 3x + 1) = 5 - x^2 + 3x - 1 = $ $-x^2 + 3x + 4$

a) $(x + 2)(x + 5) = x^2 + 5x + 2x + 10 = $ $x^2 + 7x + 10$

b) $(a + 3)(a - 4) = a^2 - 4a + 3a - 12 = $ $a^2 - a - 12$

c) $(2y - 1)(y + 6) = 2y^2 + 12y - y - 6 = $ $2y^2 + 11y - 6$

d) $(7 - b)(7 + b) = 49 + 7b - 7b - b^2 = $ $49 - b^2$

e) $(3x - 2)(2x - 5) = 6x^2 - 15x - 4x + 10 = $ $6x^2 - 19x + 10$

a) $5x + 15 = 5 \times x + 5 \times 3 = $ $5(x + 3)$

b) $3a - 6 = 3 \times a - 3 \times 2 = $ $3(a - 2)$

c) $7y + 7 = 7 \times y + 7 \times 1 = $ $7(y + 1)$

d) $x^2 + 4x = x \times x + x \times 4 = $ $x(x + 4)$

e) $12b - 18 = 6 \times 2b - 6 \times 3 = $ $6(2b - 3)$

a) $3(x + 2) + 2(x - 1) = (3x + 6) + (2x - 2) = 3x + 6 + 2x - 2 = $ $5x + 4$

b) $5(a - 1) - (3a + 4) = (5a - 5) - 3a - 4 = 5a - 5 - 3a - 4 = $ $2a - 9$

c) $(x + 1)(x + 2) + 3x = (x^2 + 2x + x + 2) + 3x = x^2 + 3x + 2 + 3x = $ $x^2 + 6x + 2$

d) $(y - 4)(y + 2) - 5y = (y^2 + 2y - 4y - 8) - 5y = y^2 - 2y - 8 - 5y = $ $y^2 - 7y - 8$

e) $2a(a - 3) - (a + 1)(a - 5) = (2a^2 - 6a) - (a^2 - 5a + a - 5) = 2a^2 - 6a - (a^2 - 4a - 5) = 2a^2 - 6a - a^2 + 4a + 5 = $ $a^2 - 2a + 5$

a) $\underline{(x + 2)}(3x - 1) + \underline{(x + 2)}(5x + 4) = (x + 2) [ (3x - 1) + (5x + 4) ] = (x + 2) [ 3x - 1 + 5x + 4 ] = $ $(x + 2)(8x + 3)$

b) $\underline{(2a - 3)}(a + 5) - \underline{(2a - 3)}(4a + 1) = (2a - 3) [ (a + 5) - (4a + 1) ] = (2a - 3) [ a + 5 - 4a - 1 ] = $ $(2a - 3)(-3a + 4)$

c) $(y + 6)^2 + (y + 6)(3y - 2) = \underline{(y + 6)}(y + 6) + \underline{(y + 6)}(3y - 2) = (y + 6) [ (y + 6) + (3y - 2) ] = (y + 6) [ y + 6 + 3y - 2 ] = $ $(y + 6)(4y + 4)$

d) $(b + 1)(2b - 5) + (b + 1) \times 1 = \underline{(b + 1)}(2b - 5) + \underline{(b + 1)} \times 1 = (b + 1) [ (2b - 5) + 1 ] = (b + 1) [ 2b - 5 + 1 ] = $ $(b + 1)(2b - 4)$

e) $(3x - 4)\underline{(x + 7)} - \underline{(x + 7)}(5x + 3) = (x + 7) [ (3x - 4) - (5x + 3) ] = (x + 7) [ 3x - 4 - 5x - 3 ] = $ $(x + 7)(-2x - 7)$