Question

4. Efectuați ridicările la putere şi reduceți termenii asemenea: a) (2x-4)² + (5x + 1)²; b) (2x-4)²2 c) (2x + 1)² + (3x - 2)²; d) (3x + 2)²-(2x + 5)²; e) (6x - 5)² + (3x+3)²; f) (3-5x)²+(4-9x)²; g) (4x-3)²-(2x-7)²; f) (7x + 2)²-(5x-6)²; h) (2-4x)²-(6+2x)².​

Answer 1

b)

$(2x-4)^2 + (5x + 1)^2\\4x^2-16x+8+25x^2+10x+1\\29x^2-6x+9$

a)

$(2x+1)^2+(3x-2)^2\\4x^2+4x+1+9x^2-12x+4\\13x^2-8x+5$

c)

$(3x+2)^2-(2x+5)^2\\9x^2+12x+4-4x^2-20x-25\\5x^2-8x-21\\\\d)\\(4x-3)^2-(2x-7)^2\\16x^2-24x+9-4x^2+28x-49\\12x^2-4x-40\\\\e)\\(6x-5)^2+(3x+3)^2\\36x^2-60x+25+9x^2+18x+9\\45x^2-42x+34\\\\f)\\(7x+2)^2-(5x-6)^2\\49x^2+28x+4-25x^2+60x-36\\24x^2+88x-32\\\\g)\\(3-5x)^2+(4-9x)^2\\9-30x+25x^2+16-62x+81x^2\\106x^2-92x+25\\\\h)\\(2-4x)^2-(6+2x)^2\\4-16x+16x^2-36-24x-4x^2\\12x^2-40x+32$

$(a-b)^2=a^2-2*a*b+b^2\\(a+b)^2=a^2+2*a*b+b^2$