Question

solve it fast . I need the answer​

Answer 1

Step-by-step explanation:

First, let's expand this.

$(a + 7)(a - 10) + 16 \\ = a^{2} + (7 - 10)a + (7)( - 10) \: \: \: + 16 \\ = ( {a }^{2} - 3a - 70 ) + 16 \\ = {a}^{2} - 3a - 54$

Then find 2 numbers which multiply to -54 and add to -3

For this, first find factors of 54 and then see which pair adds up to -3.

Factors of 54:-

±1 × ±54

±2 × ±27

±3 × ±18

±6 × ±9

Out of this, the pair

±9, ±6 does the job.

(-9) + (6) = (-3), and

(-9) × (6) = (-54)

So we spilt the middle term -3a as -9a + 6a, and we get:

${a}^{2} - 3a - 54 \\ = {a}^{2} - 9a + 6a - 54 \\ = a(a - 9) + 6(a - 9) \\ = (a - 9)(a + 6)$

And yo, they're the factors that you're looking for!

(a + 7)(a - 10) + 16 = (a - 9)(a + 6)

Hope you found my answer helpful. Keep Smiling!