Solve (2a + 3) ^ 2 + (6a - 5) ^ 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

$$(2a+3)^{2}+(6a-5)^{2}$$

Evaluate

$40a^{2}-48a+34$

Solution Steps

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

$$4a^{2}+12a+9+\left(6a-5\right)^{2}$$

Use binomial theorem $\left(p-q\right)^{2}=p^{2}-2pq+q^{2}$ to expand $\left(6a-5\right)^{2}$.

$$4a^{2}+12a+9+36a^{2}-60a+25$$

Combine $4a^{2}$ and $36a^{2}$ to get $40a^{2}$.

$$40a^{2}+12a+9-60a+25$$

Combine $12a$ and $-60a$ to get $-48a$.

$$40a^{2}-48a+9+25$$

Add $9$ and $25$ to get $34$.

$$40a^{2}-48a+34$$

Expand

$40a^{2}-48a+34$

Solution Steps

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

$$4a^{2}+12a+9+\left(6a-5\right)^{2}$$

Use binomial theorem $\left(p-q\right)^{2}=p^{2}-2pq+q^{2}$ to expand $\left(6a-5\right)^{2}$.

$$4a^{2}+12a+9+36a^{2}-60a+25$$

Combine $4a^{2}$ and $36a^{2}$ to get $40a^{2}$.

$$40a^{2}+12a+9-60a+25$$

Combine $12a$ and $-60a$ to get $-48a$.

$$40a^{2}-48a+9+25$$

Add $9$ and $25$ to get $34$.

$$40a^{2}-48a+34$$