Solve 49x^2-4(x^2-3x)^2

$$49 x ^ { 2 } - 4 ( x ^ { 2 } - 3 x ) ^ { 2 }$$

Evaluate

$$\left(13-2x\right)\left(2x+1\right)x^{2}$$

Solution Steps

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

$$49x^{2}-4\left(\left(x^{2}\right)^{2}-6x^{2}x+9x^{2}\right)$$

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

$$49x^{2}-4\left(x^{4}-6x^{2}x+9x^{2}\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$49x^{2}-4\left(x^{4}-6x^{3}+9x^{2}\right)$$

Use the distributive property to multiply -4 by x^{4}-6x^{3}+9x^{2}.

$$49x^{2}-4x^{4}+24x^{3}-36x^{2}$$

Combine 49x^{2} and -36x^{2} to get 13x^{2}.

$$13x^{2}-4x^{4}+24x^{3}$$

Expand

$$13x^{2}+24x^{3}-4x^{4}$$

Solution Steps

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

$$49x^{2}-4\left(\left(x^{2}\right)^{2}-6x^{2}x+9x^{2}\right)$$

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

$$49x^{2}-4\left(x^{4}-6x^{2}x+9x^{2}\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$49x^{2}-4\left(x^{4}-6x^{3}+9x^{2}\right)$$

Use the distributive property to multiply -4 by x^{4}-6x^{3}+9x^{2}.

$$49x^{2}-4x^{4}+24x^{3}-36x^{2}$$

Combine 49x^{2} and -36x^{2} to get 13x^{2}.

$$13x^{2}-4x^{4}+24x^{3}$$