Evaluate 8z-5z(4z-2(3z-6))-7z(-5z+3)

$8 z - 5 z (4 z - 2 (3 z - 6)) - 7 z (- 5 z + 3)$

Step 1

Simplify each term.

Apply the distributive property.

$8 z - 5 z (4 z - 2 (3 z) - 2 \cdot - 6) - 7 z (- 5 z + 3)$

Multiply $3$ by $- 2$ .

$8 z - 5 z (4 z - 6 z - 2 \cdot - 6) - 7 z (- 5 z + 3)$

Multiply $- 2$ by $- 6$ .

$8 z - 5 z (4 z - 6 z + 12) - 7 z (- 5 z + 3)$

Subtract $6 z$ from $4 z$ .

$8 z - 5 z (- 2 z + 12) - 7 z (- 5 z + 3)$

Apply the distributive property.

$8 z - 5 z (- 2 z) - 5 z \cdot 12 - 7 z (- 5 z + 3)$

Rewrite using the commutative property of multiplication.

$8 z - 5 \cdot - 2 z \cdot z - 5 z \cdot 12 - 7 z (- 5 z + 3)$

Multiply $12$ by $- 5$ .

$8 z - 5 \cdot - 2 z \cdot z - 60 z - 7 z (- 5 z + 3)$

Simplify each term.

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

Move $z$ .

$8 z - 5 \cdot - 2 (z \cdot z) - 60 z - 7 z (- 5 z + 3)$

Multiply $z$ by $z$ .

$8 z - 5 \cdot - 2 z^{2} - 60 z - 7 z (- 5 z + 3)$

Multiply $- 5$ by $- 2$ .

$8 z + 10 z^{2} - 60 z - 7 z (- 5 z + 3)$

Apply the distributive property.

$8 z + 10 z^{2} - 60 z - 7 z (- 5 z) - 7 z \cdot 3$

Rewrite using the commutative property of multiplication.

$8 z + 10 z^{2} - 60 z - 7 \cdot - 5 z \cdot z - 7 z \cdot 3$

Multiply $3$ by $- 7$ .

$8 z + 10 z^{2} - 60 z - 7 \cdot - 5 z \cdot z - 21 z$

Simplify each term.

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

Move $z$ .

$8 z + 10 z^{2} - 60 z - 7 \cdot - 5 (z \cdot z) - 21 z$

Multiply $z$ by $z$ .

$8 z + 10 z^{2} - 60 z - 7 \cdot - 5 z^{2} - 21 z$

Multiply $- 7$ by $- 5$ .

$8 z + 10 z^{2} - 60 z + 35 z^{2} - 21 z$

Step 2

Simplify by adding terms.

Subtract $60 z$ from $8 z$ .

$10 z^{2} - 52 z + 35 z^{2} - 21 z$

Add $10 z^{2}$ and $35 z^{2}$ .

$45 z^{2} - 52 z - 21 z$

Subtract $21 z$ from $- 52 z$ .

$45 z^{2} - 73 z$

Evaluate 8z-5z(4z-2(3z-6))-7z(-5z+3)

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