SENSEI AI
About App

The problem asks us to expand the expression $(2x + y - 3z)^2$.

AlgebraAlgebraic ExpansionPolynomialsMultivariable Expressions
2025/5/10

1. Problem Description

The problem asks us to expand the expression (2x+y−3z)2(2x + y - 3z)^2.

2. Solution Steps

We can use the formula (a+b+c)2=a2+b2+c2+2ab+2bc+2ca(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca.
In our case, a=2xa = 2x, b=yb = y, and c=−3zc = -3z.
Applying the formula, we get:
(2x+y−3z)2=(2x)2+(y)2+(−3z)2+2(2x)(y)+2(y)(−3z)+2(−3z)(2x)(2x + y - 3z)^2 = (2x)^2 + (y)^2 + (-3z)^2 + 2(2x)(y) + 2(y)(-3z) + 2(-3z)(2x)
=4x2+y2+9z2+4xy−6yz−12zx= 4x^2 + y^2 + 9z^2 + 4xy - 6yz - 12zx
Therefore, (2x+y−3z)2=4x2+y2+9z2+4xy−6yz−12zx(2x + y - 3z)^2 = 4x^2 + y^2 + 9z^2 + 4xy - 6yz - 12zx.

3. Final Answer

4x2+y2+9z2+4xy−6yz−12zx4x^2 + y^2 + 9z^2 + 4xy - 6yz - 12zx

Related problems in "Algebra"

Isaac and Seth share $£3600$. Seth gets twice as much money as Isaac. We need to find out how much S...

Linear EquationsWord ProblemRatio and Proportion
2025/5/10

The problem is to simplify the complex fraction $\frac{1 + \sqrt{2}i}{\sqrt{3} - 2i}$.

Complex NumbersComplex FractionsSimplificationConjugate
2025/5/10

The problem asks us to solve four systems of linear equations using the substitution method. System ...

Linear EquationsSystems of EquationsSubstitution Method
2025/5/10

The problem requires us to add two complex numbers: $(4 + i\sqrt{3})$ and $(-6 - 2i\sqrt{3})$.

Complex NumbersAdditionImaginary Numbers
2025/5/10

The problem asks us to expand the expression $(x - y - 1)(x - y + 3)$.

Polynomial ExpansionAlgebraic Manipulation
2025/5/10

Expand the expression $(x - y - 2z)^2$.

Algebraic ExpansionPolynomialsTrinomial Square
2025/5/10

The problem asks to expand the expression $(x - 2y + 3z)^2$.

Algebraic ExpansionTrinomial ExpansionPolynomials
2025/5/10

The problem asks for the degree and the constant term of the polynomial $3x^2 - 4x^2y^3 + xy^2 + y^3...

PolynomialsDegree of a polynomialConstant term
2025/5/10

The problem asks us to simplify the given expression by combining like terms: $-3x + x^2 + 9 - x^2 +...

SimplificationCombining Like TermsPolynomials
2025/5/10

Expand the expression $(x - y - 1)(x - y + 3)$.

Polynomial ExpansionAlgebraic Manipulation
2025/5/10