Question

$$(x+10)(x+10)$$ $$(3 x+5)\left(\frac{2}{3} x-3\right)$$

Short answer

The simplified form of the first expression \((x+10)(x+10)\) is \(x^2 + 20x + 100\), and the simplified form of the second expression \((3x+5)\left(\frac{2}{3}x-3\right)\) is \(2x^2 + \frac{1}{3}x - 15\).

Step-by-step solution

Solve the first expression

The first expression is \((x+10)(x+10)\). Use the FOIL method: \n\(F\): multiply \(x * x\) to get \(x^2\), \n\(O\): multiply \(x * 10\) to get \(10x\), \n\(I\): multiply \(10 * x\) to get \(10x\), \n\(L\): multiply \(10 * 10\) to get \(100\). \nAdd these together to get \(x^2 + 10x + 10x + 100 = x^2 + 20x + 100\)

Solve the second expression

The second expression is \((3x+5)\left(\frac{2}{3}x-3\right)\). Use the FOIL method: \n\(F\): multiply \(3x * \frac{2}{3}x\) to get \(2x^2\), \n\(O\): multiply \(3x * -3\) to get \(-9x\), \n\(I\): multiply \(5 * \frac{2}{3}x\) to get \(\frac{10}{3}x\), \n\(L\): multiply \(5 * -3\) to get \(-15\). \nAdd these together to get \(2x^2 - 9x + \frac{10}{3}x - 15 = 2x^2 + \frac{1}{3}x - 15\) after combining like terms.