Find the Perfect Square Trinomial (3z+2k)^2

${(3 z + 2 k)}^{2}$

Step 1

Rewrite ${(3 z + 2 k)}^{2}$ as $(3 z + 2 k) (3 z + 2 k)$ .

$(3 z + 2 k) (3 z + 2 k)$

Step 2

Expand $(3 z + 2 k) (3 z + 2 k)$ using the FOIL Method.

Apply the distributive property.

$3 z (3 z + 2 k) + 2 k (3 z + 2 k)$

Apply the distributive property.

$3 z (3 z) + 3 z (2 k) + 2 k (3 z + 2 k)$

Apply the distributive property.

$3 z (3 z) + 3 z (2 k) + 2 k (3 z) + 2 k (2 k)$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 z \cdot z + 3 z (2 k) + 2 k (3 z) + 2 k (2 k)$

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

Move $z$ .

$3 \cdot 3 (z \cdot z) + 3 z (2 k) + 2 k (3 z) + 2 k (2 k)$

Multiply $z$ by $z$ .

$3 \cdot 3 z^{2} + 3 z (2 k) + 2 k (3 z) + 2 k (2 k)$

Multiply $3$ by $3$ .

$9 z^{2} + 3 z (2 k) + 2 k (3 z) + 2 k (2 k)$

Rewrite using the commutative property of multiplication.

$9 z^{2} + 3 \cdot 2 z k + 2 k (3 z) + 2 k (2 k)$

Multiply $3$ by $2$ .

$9 z^{2} + 6 z k + 2 k (3 z) + 2 k (2 k)$

Rewrite using the commutative property of multiplication.

$9 z^{2} + 6 z k + 2 \cdot 3 k z + 2 k (2 k)$

Multiply $2$ by $3$ .

$9 z^{2} + 6 z k + 6 k z + 2 k (2 k)$

Rewrite using the commutative property of multiplication.

$9 z^{2} + 6 z k + 6 k z + 2 \cdot 2 k \cdot k$

Multiply $k$ by $k$ by adding the exponents.

Move $k$ .

$9 z^{2} + 6 z k + 6 k z + 2 \cdot 2 (k \cdot k)$

Multiply $k$ by $k$ .

$9 z^{2} + 6 z k + 6 k z + 2 \cdot 2 k^{2}$

Multiply $2$ by $2$ .

$9 z^{2} + 6 z k + 6 k z + 4 k^{2}$

Add $6 z k$ and $6 k z$ .

Move $z$ .

$9 z^{2} + 6 k z + 6 k z + 4 k^{2}$

Add $6 k z$ and $6 k z$ .

$9 z^{2} + 12 k z + 4 k^{2}$

Find the Perfect Square Trinomial (3z+2k)^2

Related Questions

Support LCMGCF.com by disabling your adblocker.