Solve =(4x^2+7x)^3

$$= ( 4 x ^ { 2 } + 7 x ) ^ { 3 }$$

Evaluate

$$\left(x\left(4x+7\right)\right)^{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(4x^{2}+7x\right)^{3}.

$$64\left(x^{2}\right)^{3}+336\left(x^{2}\right)^{2}x+588x^{2}x^{2}+343x^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$64x^{6}+336\left(x^{2}\right)^{2}x+588x^{2}x^{2}+343x^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$64x^{6}+336x^{4}x+588x^{2}x^{2}+343x^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$64x^{6}+336x^{5}+588x^{2}x^{2}+343x^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$64x^{6}+336x^{5}+588x^{4}+343x^{3}$$

Expand

$$64x^{6}+336x^{5}+588x^{4}+343x^{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(4x^{2}+7x\right)^{3}.

$$64\left(x^{2}\right)^{3}+336\left(x^{2}\right)^{2}x+588x^{2}x^{2}+343x^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$64x^{6}+336\left(x^{2}\right)^{2}x+588x^{2}x^{2}+343x^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$64x^{6}+336x^{4}x+588x^{2}x^{2}+343x^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$64x^{6}+336x^{5}+588x^{2}x^{2}+343x^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$64x^{6}+336x^{5}+588x^{4}+343x^{3}$$