Simplify (1.5x-2.4)^2-(5.2x^2-6.4)

${(1.5 x - 2.4)}^{2} - (5.2 x^{2} - 6.4)$

Simplify each term.

Rewrite ${(1.5 x - 2.4)}^{2}$ as $(1.5 x - 2.4) (1.5 x - 2.4)$ .

$(1.5 x - 2.4) (1.5 x - 2.4) - (5.2 x^{2} - 6.4)$

Expand $(1.5 x - 2.4) (1.5 x - 2.4)$ using the FOIL Method.

Apply the distributive property.

$1.5 x (1.5 x - 2.4) - 2.4 (1.5 x - 2.4) - (5.2 x^{2} - 6.4)$

Apply the distributive property.

$1.5 x (1.5 x) + 1.5 x \cdot - 2.4 - 2.4 (1.5 x - 2.4) - (5.2 x^{2} - 6.4)$

Apply the distributive property.

$1.5 x (1.5 x) + 1.5 x \cdot - 2.4 - 2.4 (1.5 x) - 2.4 \cdot - 2.4 - (5.2 x^{2} - 6.4)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$1.5 \cdot 1.5 x \cdot x + 1.5 x \cdot - 2.4 - 2.4 (1.5 x) - 2.4 \cdot - 2.4 - (5.2 x^{2} - 6.4)$

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

Move $x$ .

$1.5 \cdot 1.5 (x \cdot x) + 1.5 x \cdot - 2.4 - 2.4 (1.5 x) - 2.4 \cdot - 2.4 - (5.2 x^{2} - 6.4)$

Multiply $x$ by $x$ .

$1.5 \cdot 1.5 x^{2} + 1.5 x \cdot - 2.4 - 2.4 (1.5 x) - 2.4 \cdot - 2.4 - (5.2 x^{2} - 6.4)$

Multiply $1.5$ by $1.5$ .

$2.25 x^{2} + 1.5 x \cdot - 2.4 - 2.4 (1.5 x) - 2.4 \cdot - 2.4 - (5.2 x^{2} - 6.4)$

Multiply $- 2.4$ by $1.5$ .

$2.25 x^{2} - 3.6 x - 2.4 (1.5 x) - 2.4 \cdot - 2.4 - (5.2 x^{2} - 6.4)$

Multiply $1.5$ by $- 2.4$ .

$2.25 x^{2} - 3.6 x - 3.6 x - 2.4 \cdot - 2.4 - (5.2 x^{2} - 6.4)$

Multiply $- 2.4$ by $- 2.4$ .

$2.25 x^{2} - 3.6 x - 3.6 x + 5.76 - (5.2 x^{2} - 6.4)$

Subtract $3.6 x$ from $- 3.6 x$ .

$2.25 x^{2} - 7.2 x + 5.76 - (5.2 x^{2} - 6.4)$

Apply the distributive property.

$2.25 x^{2} - 7.2 x + 5.76 - (5.2 x^{2}) - - 6.4$

Multiply $5.2$ by $- 1$ .

$2.25 x^{2} - 7.2 x + 5.76 - 5.2 x^{2} - - 6.4$

Multiply $- 1$ by $- 6.4$ .

$2.25 x^{2} - 7.2 x + 5.76 - 5.2 x^{2} + 6.4$

Simplify by adding terms.

Subtract $5.2 x^{2}$ from $2.25 x^{2}$ .

$- 2.95 x^{2} - 7.2 x + 5.76 + 6.4$

Add $5.76$ and $6.4$ .

$- 2.95 x^{2} - 7.2 x + 12.16$