What is expand (a+bx+cy+dz)*(a-bx-cy-dz) ?

The solution to expand (a+bx+cy+dz)*(a-bx-cy-dz) is -b^2x^2-2bcxy-2bxdz+a^2-c^2y^2-2cydz-dz^2

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expand (a+bx+cy+dz)*(a-bx-cy-dz)

expand

(a + b x + cy + d z) \cdot (a - b x - cy - d z)

- b^{2} x^{2} - 2 b c x y - 2 b x d z + a^{2} - c^{2} y^{2} - 2 cy d z - d z^{2}

Solution steps

(a + b x + cy + d z) (a - b x - cy - d z)

Distribute parentheses

= aa + a (- b x) + a (- cy) + a (- d z) + b x a + b x (- b x) + b x (- cy) + b x (- d z) + cy a + cy (- b x) + cy (- cy) + cy (- d z) + d z a + d z (- b x) + d z (- cy) + d z (- d z)

Apply minus-plus rules

+ (- a) = - a

= aa - ab x - a cy - a d z + ab x - bb xx - b c x y - b x d z + a cy - b c x y - ccyy - cy d z + a d z - b x d z - cy d z - d z d z

Simplify

aa - ab x - a cy - a d z + ab x - bb xx - b c x y - b x d z + a cy - b c x y - ccyy - cy d z + a d z - b x d z - cy d z - d z d z : - b^{2} x^{2} - 2 b c x y - 2 b x d z + a^{2} - c^{2} y^{2} - 2 cy d z - d z^{2}

= - b^{2} x^{2} - 2 b c x y - 2 b x d z + a^{2} - c^{2} y^{2} - 2 cy d z - d z^{2}

\frac{\frac{d}{d x} ( - x ^{2} - 1 )}{( x ^{2} - 1 ) ^{2}}

(y cos (x) + 1) d x + sin (x) d y

\frac{( p ( 424 - p ) ^{2} )}{150}

(3 x^{2} - 2 x + 1) l e f t (x^{3} + 2 x^{2})

(- 3 + 3 i 3)^{5}

What is expand (a+bx+cy+dz)*(a-bx-cy-dz) ?
The solution to expand (a+bx+cy+dz)*(a-bx-cy-dz) is -b^2x^2-2bcxy-2bxdz+a^2-c^2y^2-2cydz-dz^2