Solve (2a - 3b) ^ 2 + 2(2a - 3b) + (2a - 3b) ^ 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

$$(2a-3b)^{2}+2(2a-3b)+(2a-3b)^{2}$$

Evaluate

$2\left(2a-3b\right)\left(2a-3b+1\right)$

Solution Steps

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

$$4a^{2}-12ab+9b^{2}+2\left(2a-3b\right)+\left(2a-3b\right)^{2}$$

Use the distributive property to multiply $2$ by $2a-3b$.

$$4a^{2}-12ab+9b^{2}+4a-6b+\left(2a-3b\right)^{2}$$

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

$$4a^{2}-12ab+9b^{2}+4a-6b+4a^{2}-12ab+9b^{2}$$

Combine $4a^{2}$ and $4a^{2}$ to get $8a^{2}$.

$$8a^{2}-12ab+9b^{2}+4a-6b-12ab+9b^{2}$$

Combine $-12ab$ and $-12ab$ to get $-24ab$.

$$8a^{2}-24ab+9b^{2}+4a-6b+9b^{2}$$

Combine $9b^{2}$ and $9b^{2}$ to get $18b^{2}$.

$$8a^{2}-24ab+18b^{2}+4a-6b$$

Expand

$8a^{2}-24ab+4a+18b^{2}-6b$

Solution Steps

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

$$4a^{2}-12ab+9b^{2}+2\left(2a-3b\right)+\left(2a-3b\right)^{2}$$

Use the distributive property to multiply $2$ by $2a-3b$.

$$4a^{2}-12ab+9b^{2}+4a-6b+\left(2a-3b\right)^{2}$$

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

$$4a^{2}-12ab+9b^{2}+4a-6b+4a^{2}-12ab+9b^{2}$$

Combine $4a^{2}$ and $4a^{2}$ to get $8a^{2}$.

$$8a^{2}-12ab+9b^{2}+4a-6b-12ab+9b^{2}$$

Combine $-12ab$ and $-12ab$ to get $-24ab$.

$$8a^{2}-24ab+9b^{2}+4a-6b+9b^{2}$$

Combine $9b^{2}$ and $9b^{2}$ to get $18b^{2}$.

$$8a^{2}-24ab+18b^{2}+4a-6b$$