Question

Expand the following
1)(4p + 5q) ³
2)(3x-2y + 4z)²
​

Answer 1

Answer:

I hope this will help you

Answer 2

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☯️QUESTION:

• (4p+5q)³
• (3x-2y+4z)²

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☯️SOLUTION:

i) (4p+5q)³

Using (a+b)³ = a³ + 3a²b + 3ab² + b³, expand the expression

$\Bigg \downarrow\Bigg \downarrow\Bigg \downarrow\Bigg \downarrow$

= (4p)³ + 3 × (4p)² × 5q + 3 × 4p × (5q)² + (5q)³

$\tt raise \: the \: product \: to \: the \: power$

$\Bigg \downarrow\Bigg \downarrow\Bigg \downarrow\Bigg \downarrow$

= 64p³ + 3 × 16p² × 5q + 3 × 4p × 25q² + 125q³

$\tt calculate \: the \: product$

$\Bigg \downarrow\Bigg \downarrow\Bigg \downarrow\Bigg \downarrow$

= 64p³ + 240p²q + 300pq² + 125q³

ANSWER:

64p³ + 240p²q + 300pq² + 125q³

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ii) (3x-2y+4z)²

Using (a+b+c)² = a² + b² + c² +2ab +2ac + 2bc, expand the expression

$\Bigg \downarrow\Bigg \downarrow\Bigg \downarrow\Bigg \downarrow$

= (3x)² + (-2y)² + (4z)² + 2(3x)(-2y) + 2(3x)(4z) +2(-2y)(4z)

$\tt raise \: the \: product \: to \: the \: power$

$\Bigg \downarrow\Bigg \downarrow\Bigg \downarrow\Bigg \downarrow$

= 9x² + 4y² + 16z² + 2(3x)(-2y) + 2(3x)(4z) +2(-2y)(4z)

$\tt calculate \: the \: product$

$\Bigg \downarrow\Bigg \downarrow\Bigg \downarrow\Bigg \downarrow$

= 9x² + 4y² + 16z² - 12xy + 24xz - 16yz

ANSWER:

9x² + 4y² + 16z² - 12xy + 24xz - 16yz

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