[latex]1.a) xy+x+2y+2 [/latex] [latex]b) 6a+2ab+3-b[/latex] [latex]c) a^{3}-ab^{2}+a^{2}+b^{2}[/latex] [latex]d) 2xy-6x-y+3[/latex] [latex]e) xa-xb+9x-ya+yb-9y[/latex] [latex]f) k^{2}t+8k^{2}-2kt-16k+2t+16[/latex] [latex]2. a) x^{2}+3x+2[/latex] [latex]b) 3a^{2}-11a-20[/latex] [latex]c) -1t-6t^{2}+1[/latex] [latex]d) 58ab-21a^{2}b^{2}-21[/latex] [latex]e) -5x^{2}-xy+6y^{2}[/latex] [latex]f) 7x^{2}+35xy-5y^{2}[/latex] [latex]g) 2x^{8}+x^{4}y-y^{2}[/latex] [latex]h) 2a^{2}b^{2} + 4a^{2}b+6a^{2}[/latex]
[latex]1.\a) (x+2)(y+1) = xy +x+2y+2\\b) (2a+1)(3-b) = 6a-2ab+3-b\\c) (a-1)(a^{2}-b^{2}) = a^{3}-ab-a^{2}+b^{2}\\d) (2x-1)(y-3) = 2xy-6x-y+3\\e) (x-y)(a-b+9) = ax-bx+9x+ay+by-9y\\f) (k^{2}-2k+2)(t+8) = tk^{2} + 8k^{2}-2tk-16k+2t+16[/latex] [latex]2.\a) (x+1)(x+2) = x^{2}+2x+x+2 = x^{2}+3x+2\\b) (3a+4)(a-5) = 3a^{2}-15a + 4a - 20 = 3a^{2}-11a-20\\c) (2t+1)(1-3t) = 2t-6t^{2}+1-3t = -6t^{2}-t+1\\d) (3ab-7)(3-7ab) = 9ab - 21a^{2}b^{2}-21+49ab = 58ab - 21a^{2}b^{2}-21\\e) (-x+y)(5x+6y) =-5x^{2}-6xy+5xy+6y^{2} = -5x^{2}-xy+6y^{2}\\f) (x+5y)(7x-y) = 7x^{2}-xy+35xy -5y^{2} = 7x^{2}+34xy-5y^{2}\\g) (2x^{4}-y)(x^{4}+y) = 2x^{8}+2x^{4}y - x^{4}y -y^{2} = 2x^{8}+x^{4}y - y^{2} [/latex] [latex]h) (ab-a)(2ab+6a) = 2a^{2}b^{2}+6a^{2}b-2a^{2}b-6a^{2} = 2a^{2}b^{2}+4a^{2}b - 6a^{2}[/latex]
