Solve 25(4x-3)^(2)-9(2x+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

$$25 { \left(4x-3 \right) }^{ 2 } -9 { \left(2x+1 \right) }^{ 2 }$$

Evaluate

$364x^{2}-636x+216$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(4x-3\right)^{2}$.

$$25\left(16x^{2}-24x+9\right)-9\left(2x+1\right)^{2}$$

Use the distributive property to multiply $25$ by $16x^{2}-24x+9$.

$$400x^{2}-600x+225-9\left(2x+1\right)^{2}$$

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

$$400x^{2}-600x+225-9\left(4x^{2}+4x+1\right)$$

Use the distributive property to multiply $-9$ by $4x^{2}+4x+1$.

$$400x^{2}-600x+225-36x^{2}-36x-9$$

Combine $400x^{2}$ and $-36x^{2}$ to get $364x^{2}$.

$$364x^{2}-600x+225-36x-9$$

Combine $-600x$ and $-36x$ to get $-636x$.

$$364x^{2}-636x+225-9$$

Subtract $9$ from $225$ to get $216$.

$$364x^{2}-636x+216$$

Expand

$364x^{2}-636x+216$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(4x-3\right)^{2}$.

$$25\left(16x^{2}-24x+9\right)-9\left(2x+1\right)^{2}$$

Use the distributive property to multiply $25$ by $16x^{2}-24x+9$.

$$400x^{2}-600x+225-9\left(2x+1\right)^{2}$$

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

$$400x^{2}-600x+225-9\left(4x^{2}+4x+1\right)$$

Use the distributive property to multiply $-9$ by $4x^{2}+4x+1$.

$$400x^{2}-600x+225-36x^{2}-36x-9$$

Combine $400x^{2}$ and $-36x^{2}$ to get $364x^{2}$.

$$364x^{2}-600x+225-36x-9$$

Combine $-600x$ and $-36x$ to get $-636x$.

$$364x^{2}-636x+225-9$$

Subtract $9$ from $225$ to get $216$.

$$364x^{2}-636x+216$$