Find the Perfect Square Trinomial (5d-7d^2t)^2

${(5 d - 7 d^{2} t)}^{2}$

Step 1

Rewrite ${(5 d - 7 d^{2} t)}^{2}$ as $(5 d - 7 d^{2} t) (5 d - 7 d^{2} t)$ .

$(5 d - 7 d^{2} t) (5 d - 7 d^{2} t)$

Step 2

Expand $(5 d - 7 d^{2} t) (5 d - 7 d^{2} t)$ using the FOIL Method.

Apply the distributive property.

$5 d (5 d - 7 d^{2} t) - 7 d^{2} t (5 d - 7 d^{2} t)$

Apply the distributive property.

$5 d (5 d) + 5 d (- 7 d^{2} t) - 7 d^{2} t (5 d - 7 d^{2} t)$

Apply the distributive property.

$5 d (5 d) + 5 d (- 7 d^{2} t) - 7 d^{2} t (5 d) - 7 d^{2} t (- 7 d^{2} t)$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 d \cdot d + 5 d (- 7 d^{2} t) - 7 d^{2} t (5 d) - 7 d^{2} t (- 7 d^{2} t)$

Multiply $d$ by $d$ by adding the exponents.

Move $d$ .

$5 \cdot 5 (d \cdot d) + 5 d (- 7 d^{2} t) - 7 d^{2} t (5 d) - 7 d^{2} t (- 7 d^{2} t)$

Multiply $d$ by $d$ .

$5 \cdot 5 d^{2} + 5 d (- 7 d^{2} t) - 7 d^{2} t (5 d) - 7 d^{2} t (- 7 d^{2} t)$

Multiply $5$ by $5$ .

$25 d^{2} + 5 d (- 7 d^{2} t) - 7 d^{2} t (5 d) - 7 d^{2} t (- 7 d^{2} t)$

Multiply $d$ by $d^{2}$ by adding the exponents.

Move $d^{2}$ .

$25 d^{2} + 5 (d^{2} d) (- 7 t) - 7 d^{2} t (5 d) - 7 d^{2} t (- 7 d^{2} t)$

Multiply $d^{2}$ by $d$ .

Raise $d$ to the power of $1$ .

$25 d^{2} + 5 (d^{2} d^{1}) (- 7 t) - 7 d^{2} t (5 d) - 7 d^{2} t (- 7 d^{2} t)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$25 d^{2} + 5 d^{2 + 1} (- 7 t) - 7 d^{2} t (5 d) - 7 d^{2} t (- 7 d^{2} t)$

Add $2$ and $1$ .

$25 d^{2} + 5 d^{3} (- 7 t) - 7 d^{2} t (5 d) - 7 d^{2} t (- 7 d^{2} t)$

Rewrite using the commutative property of multiplication.

$25 d^{2} + 5 \cdot - 7 d^{3} t - 7 d^{2} t (5 d) - 7 d^{2} t (- 7 d^{2} t)$

Multiply $5$ by $- 7$ .

$25 d^{2} - 35 d^{3} t - 7 d^{2} t (5 d) - 7 d^{2} t (- 7 d^{2} t)$

Multiply $d^{2}$ by $d$ by adding the exponents.

Move $d$ .

$25 d^{2} - 35 d^{3} t - 7 (d \cdot d^{2}) t \cdot 5 - 7 d^{2} t (- 7 d^{2} t)$

Multiply $d$ by $d^{2}$ .

Raise $d$ to the power of $1$ .

$25 d^{2} - 35 d^{3} t - 7 (d^{1} d^{2}) t \cdot 5 - 7 d^{2} t (- 7 d^{2} t)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$25 d^{2} - 35 d^{3} t - 7 d^{1 + 2} t \cdot 5 - 7 d^{2} t (- 7 d^{2} t)$

Add $1$ and $2$ .

$25 d^{2} - 35 d^{3} t - 7 d^{3} t \cdot 5 - 7 d^{2} t (- 7 d^{2} t)$

Multiply $5$ by $- 7$ .

$25 d^{2} - 35 d^{3} t - 35 d^{3} t - 7 d^{2} t (- 7 d^{2} t)$

Multiply $d^{2}$ by $d^{2}$ by adding the exponents.

Move $d^{2}$ .

$25 d^{2} - 35 d^{3} t - 35 d^{3} t - 7 (d^{2} d^{2}) t (- 7 t)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$25 d^{2} - 35 d^{3} t - 35 d^{3} t - 7 d^{2 + 2} t (- 7 t)$

Add $2$ and $2$ .

$25 d^{2} - 35 d^{3} t - 35 d^{3} t - 7 d^{4} t (- 7 t)$

Multiply $t$ by $t$ by adding the exponents.

Move $t$ .

$25 d^{2} - 35 d^{3} t - 35 d^{3} t - 7 d^{4} (t \cdot t) \cdot - 7$

Multiply $t$ by $t$ .

$25 d^{2} - 35 d^{3} t - 35 d^{3} t - 7 d^{4} t^{2} \cdot - 7$

Multiply $- 7$ by $- 7$ .

$25 d^{2} - 35 d^{3} t - 35 d^{3} t + 49 d^{4} t^{2}$

Subtract $35 d^{3} t$ from $- 35 d^{3} t$ .

$25 d^{2} - 70 d^{3} t + 49 d^{4} t^{2}$

Find the Perfect Square Trinomial (5d-7d^2t)^2

Related Questions

Support LCMGCF.com by disabling your adblocker.