Datrys left(5x-2right)^2-left(3x+1right)^2-x^2-60

$${ \left(5x-2 \right) }^{ 2 } - { \left(3x+1 \right) }^{ 2 } - { x }^{ 2 } -60$$

Enrhifo

$$\left(x-3\right)\left(15x+19\right)$$

Camau Ateb

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(5x-2\right)^{2}.

$$25x^{2}-20x+4-\left(3x+1\right)^{2}-x^{2}-60$$

Defnyddio'r theorem binomaidd \left(a+b\right)^{2}=a^{2}+2ab+b^{2} i ehangu'r \left(3x+1\right)^{2}.

$$25x^{2}-20x+4-\left(9x^{2}+6x+1\right)-x^{2}-60$$

I ddod o hyd i wrthwyneb 9x^{2}+6x+1, dewch o hyd i wrthwyneb pob term.

$$25x^{2}-20x+4-9x^{2}-6x-1-x^{2}-60$$

Cyfuno 25x^{2} a -9x^{2} i gael 16x^{2}.

$$16x^{2}-20x+4-6x-1-x^{2}-60$$

Cyfuno -20x a -6x i gael -26x.

$$16x^{2}-26x+4-1-x^{2}-60$$

Tynnu 1 o 4 i gael 3.

$$16x^{2}-26x+3-x^{2}-60$$

Cyfuno 16x^{2} a -x^{2} i gael 15x^{2}.

$$15x^{2}-26x+3-60$$

Tynnu 60 o 3 i gael -57.

$$15x^{2}-26x-57$$

Ehangu

$$15x^{2}-26x-57$$

Camau Ateb

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(5x-2\right)^{2}.

$$25x^{2}-20x+4-\left(3x+1\right)^{2}-x^{2}-60$$

Defnyddio'r theorem binomaidd \left(a+b\right)^{2}=a^{2}+2ab+b^{2} i ehangu'r \left(3x+1\right)^{2}.

$$25x^{2}-20x+4-\left(9x^{2}+6x+1\right)-x^{2}-60$$

I ddod o hyd i wrthwyneb 9x^{2}+6x+1, dewch o hyd i wrthwyneb pob term.

$$25x^{2}-20x+4-9x^{2}-6x-1-x^{2}-60$$

Cyfuno 25x^{2} a -9x^{2} i gael 16x^{2}.

$$16x^{2}-20x+4-6x-1-x^{2}-60$$

Cyfuno -20x a -6x i gael -26x.

$$16x^{2}-26x+4-1-x^{2}-60$$

Tynnu 1 o 4 i gael 3.

$$16x^{2}-26x+3-x^{2}-60$$

Cyfuno 16x^{2} a -x^{2} i gael 15x^{2}.

$$15x^{2}-26x+3-60$$

Tynnu 60 o 3 i gael -57.

$$15x^{2}-26x-57$$