Question

(x-8)^2 i need step by step please like eveyone gets x2 -16x +64 i dont get
how

Answer 1

x²-16x+64

• use formula =a²-2ab+b²
• x²-2.x.8+8² (for knowledge 2 × 8 = 16)
• x²-16x+64

Answer 2

(x -8)² = x² -16x +64

Explanation:

A lot of math is about pattern recognition. For many of the patterns you are asked to recognize, it is helpful to be very familiar with basic math facts: addition facts, multiplication facts, and the squares and cubes of small integers.

All of algebra is based on a few properties of arithmetic and equality. One that is important here is the distributive property.

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expanding a product of binomials

One of the patterns that is used with quadratics is the square of a binomial.

(a - b)² = a² -2ab +b²

This is the result of applying the distributive property several times.

First of all, the exponent indicates repeated multiplication:

(a -b)² = (a -b)×(a -b)

The distributive property tells you each term outside parentheses multiplies each term inside:

= a×(a -b) -b×(a -b)

= a·a -a·b -b·a +b·b . . . . . and again

Now, we collect terms, recognizing that ab=ba.

= a² -2(a·b) +b² . . . . . . . using exponents for repeated multiplication

So, the pattern for the square of a binomial is ...

(a -b)² = a² -2ab +b²

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using the pattern

For your specific case, ...

• a = x
• b = 8

(x -8)² = x² -2(x)(8) +8² . . . . . . using the above pattern

(x -8)² = x² -16x +64

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Additional comment

If you want to do this without using the pattern, just make use of the distributive property:

`(x-8)^2=(x-8)(x-8)\\\\=x(x -8) -8(x-8)\\\\=x^2-8x-(8x-64)\\\\=x^2-8x-8x+64\\\\\boxed{(x-8)^2=x^2-16x+64}}`

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While the distributive property is the fundamental property involved, some find it helpful to remember a mnemonic that gets you to the same result for the product of binomials: FOIL. The letters refer to First, Outer, Inner, Last, and they remind you of the terms that make up the expansion of the product:

• (x -8)(x -8) -- First: x·x = x²
• (x -8)(x -8) -- Outer: x·(-8) = -8x
• (x -8)(x -8) -- Inner: (-8)·x = -8x
• (x -8)(x -8) -- Last: (-8)(-8) = 64

Then the product is ...

(x -8)² = x² -8x -8x +64 = x² -16x +64

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Of course, the distributive property is involved in what we call "collecting terms."

-8x -8x = (-8-8)x = -16x

The variable is factored out using the distributive property, then the coefficients are added to simplify the expression in parentheses.