Solve 7a^2+50ab+7b^2

$$7 a ^ { 2 } + 50 a b + 7 b ^ { 2 }$$

Factor

$$\left(a+7b\right)\left(7a+b\right)$$

Solution Steps

Consider 7a^{2}+50ab+7b^{2} as a polynomial over variable a.

$$7a^{2}+50ba+7b^{2}$$

Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power 7a^{2} and n divides the constant factor 7b^{2}. One such factor is 7a+b. Factor the polynomial by dividing it by this factor.

$$\left(7a+b\right)\left(a+7b\right)$$

Evaluate

$$\left(a+7b\right)\left(7a+b\right)$$