Solve 100a^2-36(b-c)^2

$$100 a ^ { 2 } - 36 ( b - c ) ^ { 2 }$$

Evaluate

$$-36\left(c-b\right)^{2}+100a^{2}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(b-c\right)^{2}.

$$100a^{2}-36\left(b^{2}-2bc+c^{2}\right)$$

Use the distributive property to multiply -36 by b^{2}-2bc+c^{2}.

$$100a^{2}-36b^{2}+72bc-36c^{2}$$

Expand

$$100a^{2}-36b^{2}+72bc-36c^{2}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(b-c\right)^{2}.

$$100a^{2}-36\left(b^{2}-2bc+c^{2}\right)$$

Use the distributive property to multiply -36 by b^{2}-2bc+c^{2}.

$$100a^{2}-36b^{2}+72bc-36c^{2}$$