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

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

Evaluate

$9a^{2}$

Solution Steps

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

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

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

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

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

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

Use the distributive property to multiply $-4a-6b$ by $3b-a$ and combine like terms.

$$4a^{2}+12ab+9b^{2}-6ab+4a^{2}-18b^{2}+9b^{2}-6ba+a^{2}$$

Combine $12ab$ and $-6ab$ to get $6ab$.

$$4a^{2}+6ab+9b^{2}+4a^{2}-18b^{2}+9b^{2}-6ba+a^{2}$$

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

$$8a^{2}+6ab+9b^{2}-18b^{2}+9b^{2}-6ba+a^{2}$$

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

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

Combine $-9b^{2}$ and $9b^{2}$ to get $0$.

$$8a^{2}+6ab-6ba+a^{2}$$

Combine $6ab$ and $-6ba$ to get $0$.

$$8a^{2}+a^{2}$$

Combine $8a^{2}$ and $a^{2}$ to get $9a^{2}$.

$$9a^{2}$$

Expand

$9a^{2}$

Solution Steps

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

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

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

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

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

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

Use the distributive property to multiply $-4a-6b$ by $3b-a$ and combine like terms.

$$4a^{2}+12ab+9b^{2}-6ab+4a^{2}-18b^{2}+9b^{2}-6ba+a^{2}$$

Combine $12ab$ and $-6ab$ to get $6ab$.

$$4a^{2}+6ab+9b^{2}+4a^{2}-18b^{2}+9b^{2}-6ba+a^{2}$$

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

$$8a^{2}+6ab+9b^{2}-18b^{2}+9b^{2}-6ba+a^{2}$$

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

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

Combine $-9b^{2}$ and $9b^{2}$ to get $0$.

$$8a^{2}+6ab-6ba+a^{2}$$

Combine $6ab$ and $-6ba$ to get $0$.

$$8a^{2}+a^{2}$$

Combine $8a^{2}$ and $a^{2}$ to get $9a^{2}$.

$$9a^{2}$$