Question

High Order Thinking Skills (HOTS)
. 10. What should be added to (x – 4) (x + 6) to get
the product (x – 3) (x - 8)?​

Answer 1

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We have a product and we need to compute for what to be added to get another product.

• Addend = (x - 4)(x + 6)
• Sum = (x - 3)(x - 8)

Let S is to be added with the addend to get the desired sum. According to this,

⇛ (x - 4)(x + 6) + S = (x - 3)(x - 8)

⇛ S = (x - 3)(x - 8) - (x - 4)(x + 6)

Expanding the parentheses,

⇛ S = x² - 3x - 8x + 24 - (x² + 6x - 4x - 24)

⇛ S = x² - 3x - 8x + 24 - x² - 6x + 4x + 24

Now arranging the like terms to get S:

⇛ S = x² - x² - 3x - 8x - 6x + 4x + 24 + 24

⇛ S = -13x + 48

Thus, We need to add -13x + 48 with (x - 4)(x + 6) to get the sum (x - 3)(x - 8).

Answer 2

Solution

Let, y should be added to (x – 4) (x + 6) to get the product (x – 3) (x - 8)

ATP

y+(x-4)(x+6) = (x-3)(x-8)

=) y+x²+6x-4x-24 = x²-8x-3x+24

=) y+x²+2x-24 = x²-11x+24

=) y = x²-11x+24-(x²+2x-24)

=) y = x²-11x+24-x²-2x+24

=) y = -13x+48

Ans:- -13x+48 is the number which should be added to (x – 4) (x + 6) to get

the product (x – 3) (x - 8)?