en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Algebra >

expand α^2β^2(αβ+α+β+1)^2

Solution

expand

α^{2} β^{2} (α β + α + β + 1)^{2}

Solution

α^{4} β^{4} + 2 α^{3} β^{4} + 2 α^{4} β^{3} + 4 α^{3} β^{3} + α^{4} β^{2} + 2 α^{3} β^{2} + α^{2} β^{4} + 2 α^{2} β^{3} + α^{2} β^{2}

Solution steps

α^{2} β^{2} (α β + α + β + 1)^{2}

Apply exponent rule:

a^{m} b^{m} = (ab)^{m},

assuming

a \geq 0, b \geq 0

α^{2} β^{2} (α β + α + β + 1)^{2} = (α β (α β + α + β + 1))^{2}

= (α β (α β + α + β + 1))^{2}

Expand

α β (α β + α + β + 1) : α^{2} β^{2} + α^{2} β + α β^{2} + α β

= (α^{2} β^{2} + α^{2} β + α β^{2} + α β)^{2}

(α^{2} β^{2} + α^{2} β + α β^{2} + α β)^{2} = (α^{2} β^{2} + α^{2} β + α β^{2} + α β) (α^{2} β^{2} + α^{2} β + α β^{2} + α β)

= (α^{2} β^{2} + α^{2} β + α β^{2} + α β) (α^{2} β^{2} + α^{2} β + α β^{2} + α β)

Expand

(α^{2} β^{2} + α^{2} β + α β^{2} + α β) (α^{2} β^{2} + α^{2} β + α β^{2} + α β) : α^{4} β^{4} + 2 α^{3} β^{4} + 2 α^{4} β^{3} + 4 α^{3} β^{3} + α^{4} β^{2} + 2 α^{3} β^{2} + α^{2} β^{4} + 2 α^{2} β^{3} + α^{2} β^{2}

= α^{4} β^{4} + 2 α^{3} β^{4} + 2 α^{4} β^{3} + 4 α^{3} β^{3} + α^{4} β^{2} + 2 α^{3} β^{2} + α^{2} β^{4} + 2 α^{2} β^{3} + α^{2} β^{2}

Popular Examples

expand (x^2-4)dx

e x p an d (x^{2} - 4) d x

derivative of (0(12x^3-24x))

\frac{d}{d x} ((0) (12 x^{3} - 24 x))

expand 4(e^{3x}+3e^{3x}x)

e x p an d 4 (e^{3 x} + 3 e^{3 x} x)

(\partial)/(\partial x)((xy)(ey+2z))

\frac{\partial}{\partial x} ((x y) (ey + 2 z))

expand (3x+y)dx+2xdy

e x p an d (3 x + y) d x + 2 x d y

Popular topics

imaginary number calculator ratio test calculator asymptote calculator remainder calculator linear approximation calculator rational equation calculator absolute value calculator riemann sum calculator acceleration calculator area between curves calculator domain and range calculator sequence calculator integration by parts calculator slope intercept form calculator eigenvector calculator trig identities calculator power series calculator transformation calculator hours calculator parabola calculator percentage calculator average rate of change calculator age calculator volume calculator chain rule calculator concavity calculator row echelon form calculator p value calculator end behavior calculator fourier transform calculator trinomial calculator factor by grouping calculator improper integral calculator rational number calculator multiplying polynomials calculator variable calculator pemdas calculator pythagorean theorem calculator function calculator u substitution calculator