Question

3. Rút gọn biểu thức
a) $(7 x+4)^2-(7 x+4)(7 x-4)$.
b) $(6 x-2)^2+(2-5 x)^2+2(6 x-2)(2-5 x)$.
c) $(2 x-1)^2+(2 x+1)^2+2\left(4 x^2-1\right)+3$.
d) $5 \cdot(2 x-1)^2+4 \cdot(x-1)(x+3)-2 \cdot(5-3 x)^2$.

Answer 1

`a) (7x+4)^{2} - (7x+4)(7x-4)`

`=49x^{2}+56x+16-(49x^{2}-16)`

`=49x^{2}+56x+16-49x^{2}+16`

`=56x+32`

`b) (6x-2)^{2}+(2-5x)^{2}+2(6x-2)(2-5x)`

`=[(6x-2)+(2-5x)]^{2]`

`=(6x-2+2-5x)^{2}`

`=x^{2}`

Answer 2

 

c: \(\left(2x-1\right)^2+\left(2x+1\right)^2+2\left(4x^2-1\right)+3\)

\(=\left(2x-1\right)^2+2\cdot\left(2x-1\right)\left(2x+1\right)+\left(2x+1\right)^2+3\)

\(=\left(2x-1+2x+1\right)^2+3=\left(4x\right)^2+3=16x^2+3\)

d: \(5\left(2x-1\right)^2+4\left(x-1\right)\left(x+3\right)-2\left(5-3x\right)^2\)

\(=5\left(4x^2-4x+1\right)+4\left(x^2+2x-3\right)-2\left(9x^2-30x+25\right)\)

\(=20x^2-20x+5+4x^2+8x-12-18x^2+60x-50\)

\(=6x^2+48x-57\)