Solve 21a^2+42a

$$21 a ^ { 2 } + 42 a$$

Factor

$$21a\left(a+2\right)$$

Solution Steps

Factor out 21.

$$21\left(a^{2}+2a\right)$$

Consider a^{2}+2a. Factor out a.

$$a\left(a+2\right)$$

Rewrite the complete factored expression.

$$21a\left(a+2\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$21a^{2}+42a=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$a=\frac{-42±\sqrt{42^{2}}}{2\times 21}$$

Take the square root of 42^{2}.

$$a=\frac{-42±42}{2\times 21}$$

Multiply 2 times 21.

$$a=\frac{-42±42}{42}$$

Now solve the equation a=\frac{-42±42}{42} when ± is plus. Add -42 to 42.

$$a=\frac{0}{42}$$

Divide 0 by 42.

$$a=0$$

Now solve the equation a=\frac{-42±42}{42} when ± is minus. Subtract 42 from -42.

$$a=-\frac{84}{42}$$

Divide -84 by 42.

$$a=-2$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and -2 for x_{2}.

$$21a^{2}+42a=21a\left(a-\left(-2\right)\right)$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$21a^{2}+42a=21a\left(a+2\right)$$

Evaluate

$$21a\left(a+2\right)$$