Solve (2a-2/3b)(-2a-2/3b)

$$( 2 a - \frac { 2 } { 3 } b ) ( - 2 a - \frac { 2 } { 3 } b )$$

Evaluate

$$\frac{4b^{2}}{9}-4a^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 2a-\frac{2}{3}b by each term of -2a-\frac{2}{3}b.

$$-4a^{2}+2a\left(-\frac{2}{3}\right)b-\frac{2}{3}b\left(-2\right)a-\frac{2}{3}b\left(-\frac{2}{3}\right)b$$

Multiply b and b to get b^{2}.

$$-4a^{2}+2a\left(-\frac{2}{3}\right)b-\frac{2}{3}b\left(-2\right)a-\frac{2}{3}b^{2}\left(-\frac{2}{3}\right)$$

Express 2\left(-\frac{2}{3}\right) as a single fraction.

$$-4a^{2}+\frac{2\left(-2\right)}{3}ab-\frac{2}{3}b\left(-2\right)a-\frac{2}{3}b^{2}\left(-\frac{2}{3}\right)$$

Multiply 2 and -2 to get -4.

$$-4a^{2}+\frac{-4}{3}ab-\frac{2}{3}b\left(-2\right)a-\frac{2}{3}b^{2}\left(-\frac{2}{3}\right)$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$-4a^{2}-\frac{4}{3}ab-\frac{2}{3}b\left(-2\right)a-\frac{2}{3}b^{2}\left(-\frac{2}{3}\right)$$

Express -\frac{2}{3}\left(-2\right) as a single fraction.

$$-4a^{2}-\frac{4}{3}ab+\frac{-2\left(-2\right)}{3}ba-\frac{2}{3}b^{2}\left(-\frac{2}{3}\right)$$

Multiply -2 and -2 to get 4.

$$-4a^{2}-\frac{4}{3}ab+\frac{4}{3}ba-\frac{2}{3}b^{2}\left(-\frac{2}{3}\right)$$

Combine -\frac{4}{3}ab and \frac{4}{3}ba to get 0.

$$-4a^{2}-\frac{2}{3}b^{2}\left(-\frac{2}{3}\right)$$

Multiply -\frac{2}{3} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$-4a^{2}+\frac{-2\left(-2\right)}{3\times 3}b^{2}$$

Do the multiplications in the fraction \frac{-2\left(-2\right)}{3\times 3}.

$$-4a^{2}+\frac{4}{9}b^{2}$$

Expand

$$\frac{4b^{2}}{9}-4a^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 2a-\frac{2}{3}b by each term of -2a-\frac{2}{3}b.

$$-4a^{2}+2a\left(-\frac{2}{3}\right)b-\frac{2}{3}b\left(-2\right)a-\frac{2}{3}b\left(-\frac{2}{3}\right)b$$

Multiply b and b to get b^{2}.

$$-4a^{2}+2a\left(-\frac{2}{3}\right)b-\frac{2}{3}b\left(-2\right)a-\frac{2}{3}b^{2}\left(-\frac{2}{3}\right)$$

Express 2\left(-\frac{2}{3}\right) as a single fraction.

$$-4a^{2}+\frac{2\left(-2\right)}{3}ab-\frac{2}{3}b\left(-2\right)a-\frac{2}{3}b^{2}\left(-\frac{2}{3}\right)$$

Multiply 2 and -2 to get -4.

$$-4a^{2}+\frac{-4}{3}ab-\frac{2}{3}b\left(-2\right)a-\frac{2}{3}b^{2}\left(-\frac{2}{3}\right)$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$-4a^{2}-\frac{4}{3}ab-\frac{2}{3}b\left(-2\right)a-\frac{2}{3}b^{2}\left(-\frac{2}{3}\right)$$

Express -\frac{2}{3}\left(-2\right) as a single fraction.

$$-4a^{2}-\frac{4}{3}ab+\frac{-2\left(-2\right)}{3}ba-\frac{2}{3}b^{2}\left(-\frac{2}{3}\right)$$

Multiply -2 and -2 to get 4.

$$-4a^{2}-\frac{4}{3}ab+\frac{4}{3}ba-\frac{2}{3}b^{2}\left(-\frac{2}{3}\right)$$

Combine -\frac{4}{3}ab and \frac{4}{3}ba to get 0.

$$-4a^{2}-\frac{2}{3}b^{2}\left(-\frac{2}{3}\right)$$

Multiply -\frac{2}{3} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$-4a^{2}+\frac{-2\left(-2\right)}{3\times 3}b^{2}$$

Do the multiplications in the fraction \frac{-2\left(-2\right)}{3\times 3}.

$$-4a^{2}+\frac{4}{9}b^{2}$$