Solve 16 * (2x + 1) ^ 3 - 9(2x + 1) | 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

$$.16(2x+1)^{3}-9(2x+1)$$

Evaluate

$\frac{32x^{3}+48x^{2}-426x-221}{25}$

Solution Steps

Use binomial theorem $\left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}$ to expand $\left(2x+1\right)^{3}$.

$$0.16\left(8x^{3}+12x^{2}+6x+1\right)-9\left(2x+1\right)$$

Use the distributive property to multiply $0.16$ by $8x^{3}+12x^{2}+6x+1$.

$$1.28x^{3}+1.92x^{2}+0.96x+0.16-9\left(2x+1\right)$$

Use the distributive property to multiply $-9$ by $2x+1$.

$$1.28x^{3}+1.92x^{2}+0.96x+0.16-18x-9$$

Combine $0.96x$ and $-18x$ to get $-17.04x$.

$$1.28x^{3}+1.92x^{2}-17.04x+0.16-9$$

Subtract $9$ from $0.16$ to get $-8.84$.

$$1.28x^{3}+1.92x^{2}-17.04x-8.84$$

Expand

$\frac{32x^{3}+48x^{2}-426x-221}{25}$

Solution Steps

Use binomial theorem $\left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}$ to expand $\left(2x+1\right)^{3}$.

$$0.16\left(8x^{3}+12x^{2}+6x+1\right)-9\left(2x+1\right)$$

Use the distributive property to multiply $0.16$ by $8x^{3}+12x^{2}+6x+1$.

$$1.28x^{3}+1.92x^{2}+0.96x+0.16-9\left(2x+1\right)$$

Use the distributive property to multiply $-9$ by $2x+1$.

$$1.28x^{3}+1.92x^{2}+0.96x+0.16-18x-9$$

Combine $0.96x$ and $-18x$ to get $-17.04x$.

$$1.28x^{3}+1.92x^{2}-17.04x+0.16-9$$

Subtract $9$ from $0.16$ to get $-8.84$.

$$1.28x^{3}+1.92x^{2}-17.04x-8.84$$