Solve 2 * (p - 3) ^ 2 - 3 * (p + 1) ^ 2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$2(p-3)^{2}-3(p+1)^{2}$$

Evaluate

$15-18p-p^{2}$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(p-3\right)^{2}$.

$$2\left(p^{2}-6p+9\right)-3\left(p+1\right)^{2}$$

Use the distributive property to multiply $2$ by $p^{2}-6p+9$.

$$2p^{2}-12p+18-3\left(p+1\right)^{2}$$

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(p+1\right)^{2}$.

$$2p^{2}-12p+18-3\left(p^{2}+2p+1\right)$$

Use the distributive property to multiply $-3$ by $p^{2}+2p+1$.

$$2p^{2}-12p+18-3p^{2}-6p-3$$

Combine $2p^{2}$ and $-3p^{2}$ to get $-p^{2}$.

$$-p^{2}-12p+18-6p-3$$

Combine $-12p$ and $-6p$ to get $-18p$.

$$-p^{2}-18p+18-3$$

Subtract $3$ from $18$ to get $15$.

$$-p^{2}-18p+15$$

Expand

$15-18p-p^{2}$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(p-3\right)^{2}$.

$$2\left(p^{2}-6p+9\right)-3\left(p+1\right)^{2}$$

Use the distributive property to multiply $2$ by $p^{2}-6p+9$.

$$2p^{2}-12p+18-3\left(p+1\right)^{2}$$

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(p+1\right)^{2}$.

$$2p^{2}-12p+18-3\left(p^{2}+2p+1\right)$$

Use the distributive property to multiply $-3$ by $p^{2}+2p+1$.

$$2p^{2}-12p+18-3p^{2}-6p-3$$

Combine $2p^{2}$ and $-3p^{2}$ to get $-p^{2}$.

$$-p^{2}-12p+18-6p-3$$

Combine $-12p$ and $-6p$ to get $-18p$.

$$-p^{2}-18p+18-3$$

Subtract $3$ from $18$ to get $15$.

$$-p^{2}-18p+15$$