Find the Perfect Square Trinomial (4xy-3z)^2

${(4 x y - 3 z)}^{2}$

Step 1

Rewrite ${(4 x y - 3 z)}^{2}$ as $(4 x y - 3 z) (4 x y - 3 z)$ .

$(4 x y - 3 z) (4 x y - 3 z)$

Step 2

Expand $(4 x y - 3 z) (4 x y - 3 z)$ using the FOIL Method.

Apply the distributive property.

$4 x y (4 x y - 3 z) - 3 z (4 x y - 3 z)$

Apply the distributive property.

$4 x y (4 x y) + 4 x y (- 3 z) - 3 z (4 x y - 3 z)$

Apply the distributive property.

$4 x y (4 x y) + 4 x y (- 3 z) - 3 z (4 x y) - 3 z (- 3 z)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$4 (x \cdot x) y (4 y) + 4 x y (- 3 z) - 3 z (4 x y) - 3 z (- 3 z)$

Multiply $x$ by $x$ .

$4 x^{2} y (4 y) + 4 x y (- 3 z) - 3 z (4 x y) - 3 z (- 3 z)$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$4 x^{2} (y \cdot y) \cdot 4 + 4 x y (- 3 z) - 3 z (4 x y) - 3 z (- 3 z)$

Multiply $y$ by $y$ .

$4 x^{2} y^{2} \cdot 4 + 4 x y (- 3 z) - 3 z (4 x y) - 3 z (- 3 z)$

Multiply $4$ by $4$ .

$16 x^{2} y^{2} + 4 x y (- 3 z) - 3 z (4 x y) - 3 z (- 3 z)$

Multiply $- 3$ by $4$ .

$16 x^{2} y^{2} - 12 x y z - 3 z (4 x y) - 3 z (- 3 z)$

Multiply $4$ by $- 3$ .

$16 x^{2} y^{2} - 12 x y z - 12 z (x y) - 3 z (- 3 z)$

Rewrite using the commutative property of multiplication.

$16 x^{2} y^{2} - 12 x y z - 12 z x y - 3 \cdot - 3 z \cdot z$

Multiply $z$ by $z$ by adding the exponents.

Move $z$ .

$16 x^{2} y^{2} - 12 x y z - 12 z x y - 3 \cdot - 3 (z \cdot z)$

Multiply $z$ by $z$ .

$16 x^{2} y^{2} - 12 x y z - 12 z x y - 3 \cdot - 3 z^{2}$

Multiply $- 3$ by $- 3$ .

$16 x^{2} y^{2} - 12 x y z - 12 z x y + 9 z^{2}$

Subtract $12 z x y$ from $- 12 x y z$ .

Move $z$ .

$16 x^{2} y^{2} - 12 x y z - 12 x y z + 9 z^{2}$

Subtract $12 x y z$ from $- 12 x y z$ .

$16 x^{2} y^{2} - 24 x y z + 9 z^{2}$