Write an expression for the area of the shape and simplify it.
Write an expression for the area of the shape and simplify it.
Dividiamo la figura in due rettangoli di area A1 e A2;
A1 = (3x + 2) * (x - 1);
A2 = (x + 1) * [(2x + 1) - (x - 1)] = (x + 1) * [2x + 1 - x + 1];
A2 = (x + 1) * (x + 2);
A1 + A2 = (3x + 2) * (x - 1) + (x + 1) * (x + 2);
A1 + A2 = 3x^2 - 3x + 2x - 2 + x^2 + 2x + x + 2;
A1 + A2 = 3x^2 + x^2 - 3x + 2x + 2x + x - 2 + 2;
A1 + A2 = 4x^2 + 2x .
Ciao @francesco_boccia01
(3x+2)(x-1) + (2x + 1 - x + 1)(x+1)=
= (3x+2)(x-1) + (x+2)(x+1)= (svolgi operazioni)
= 3x**2 - 3x + 2x - 2 + x**2 + x + 2x +2 = (semplifica)
= 4x**2 + 2x
Area quadrato: $(2x+1)(x+1)=2x^2+2x+x+1=2x^2+3x+1$
Base rettangolo: $(3x+2)-(x+1)=3x+2-x-1=2x+1$
Area rettangolo: $(2x+1)(x-1)=2x^2-2x+x-1=2x^2-x-1$
Area totale: $2x^2-x-1+2x^2+3x+1=4x^2+2x (= 2x(2x+1))$