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Pre-Algebra Examples
20(r+t)320(r+t)3 , 16(r+t)616(r+t)6
Step 1
Use the Binomial Theorem.
20(r3+3r2t+3rt2+t3),16(r+t)620(r3+3r2t+3rt2+t3),16(r+t)6
Apply the distributive property.
20r3+20(3r2t)+20(3rt2)+20t3,16(r+t)620r3+20(3r2t)+20(3rt2)+20t3,16(r+t)6
Simplify.
Multiply 33 by 2020.
20r3+60(r2t)+20(3rt2)+20t3,16(r+t)620r3+60(r2t)+20(3rt2)+20t3,16(r+t)6
Multiply 33 by 2020.
20r3+60(r2t)+60(rt2)+20t3,16(r+t)620r3+60(r2t)+60(rt2)+20t3,16(r+t)6
20r3+60(r2t)+60(rt2)+20t3,16(r+t)620r3+60(r2t)+60(rt2)+20t3,16(r+t)6
Remove parentheses.
20r3+60r2t+60rt2+20t3,16(r+t)620r3+60r2t+60rt2+20t3,16(r+t)6
Use the Binomial Theorem.
20r3+60r2t+60rt2+20t3,16(r6+6r5t+15r4t2+20r3t3+15r2t4+6rt5+t6)20r3+60r2t+60rt2+20t3,16(r6+6r5t+15r4t2+20r3t3+15r2t4+6rt5+t6)
Apply the distributive property.
20r3+60r2t+60rt2+20t3,16r6+16(6r5t)+16(15r4t2)+16(20r3t3)+16(15r2t4)+16(6rt5)+16t620r3+60r2t+60rt2+20t3,16r6+16(6r5t)+16(15r4t2)+16(20r3t3)+16(15r2t4)+16(6rt5)+16t6
Simplify.
Multiply 66 by 1616.
20r3+60r2t+60rt2+20t3,16r6+96(r5t)+16(15r4t2)+16(20r3t3)+16(15r2t4)+16(6rt5)+16t620r3+60r2t+60rt2+20t3,16r6+96(r5t)+16(15r4t2)+16(20r3t3)+16(15r2t4)+16(6rt5)+16t6
Multiply 1515 by 1616.
20r3+60r2t+60rt2+20t3,16r6+96(r5t)+240(r4t2)+16(20r3t3)+16(15r2t4)+16(6rt5)+16t620r3+60r2t+60rt2+20t3,16r6+96(r5t)+240(r4t2)+16(20r3t3)+16(15r2t4)+16(6rt5)+16t6
Multiply 2020 by 1616.
20r3+60r2t+60rt2+20t3,16r6+96(r5t)+240(r4t2)+320(r3t3)+16(15r2t4)+16(6rt5)+16t620r3+60r2t+60rt2+20t3,16r6+96(r5t)+240(r4t2)+320(r3t3)+16(15r2t4)+16(6rt5)+16t6
Multiply 1515 by 1616.
20r3+60r2t+60rt2+20t3,16r6+96(r5t)+240(r4t2)+320(r3t3)+240(r2t4)+16(6rt5)+16t620r3+60r2t+60rt2+20t3,16r6+96(r5t)+240(r4t2)+320(r3t3)+240(r2t4)+16(6rt5)+16t6
Multiply 66 by 1616.
20r3+60r2t+60rt2+20t3,16r6+96(r5t)+240(r4t2)+320(r3t3)+240(r2t4)+96(rt5)+16t620r3+60r2t+60rt2+20t3,16r6+96(r5t)+240(r4t2)+320(r3t3)+240(r2t4)+96(rt5)+16t6
20r3+60r2t+60rt2+20t3,16r6+96(r5t)+240(r4t2)+320(r3t3)+240(r2t4)+96(rt5)+16t6
Remove parentheses.
20r3+60r2t+60rt2+20t3,16r6+96r5t+240r4t2+320r3t3+240r2t4+96rt5+16t6
20r3+60r2t+60rt2+20t3,16r6+96r5t+240r4t2+320r3t3+240r2t4+96rt5+16t6
Step 2
Factor out the GCF of 4 from each term in the polynomial.
Factor out the GCF of 4 from the expression 20r3.
4(5r3)+60r2t+60rt2+20t3+16r6+96r5t+240r4t2+320r3t3+240r2t4+96rt5+16t6
Factor out the GCF of 4 from the expression 60r2t.
4(5r3)+4(15r2t)+60rt2+20t3+16r6+96r5t+240r4t2+320r3t3+240r2t4+96rt5+16t6
Factor out the GCF of 4 from the expression 60rt2.
4(5r3)+4(15r2t)+4(15rt2)+20t3+16r6+96r5t+240r4t2+320r3t3+240r2t4+96rt5+16t6
Factor out the GCF of 4 from the expression 20t3.
4(5r3)+4(15r2t)+4(15rt2)+4(5t3)+16r6+96r5t+240r4t2+320r3t3+240r2t4+96rt5+16t6
Factor out the GCF of 4 from the expression 16r6.
4(5r3)+4(15r2t)+4(15rt2)+4(5t3)+4(4r6)+96r5t+240r4t2+320r3t3+240r2t4+96rt5+16t6
Factor out the GCF of 4 from the expression 96r5t.
4(5r3)+4(15r2t)+4(15rt2)+4(5t3)+4(4r6)+4(24r5t)+240r4t2+320r3t3+240r2t4+96rt5+16t6
Factor out the GCF of 4 from the expression 240r4t2.
4(5r3)+4(15r2t)+4(15rt2)+4(5t3)+4(4r6)+4(24r5t)+4(60r4t2)+320r3t3+240r2t4+96rt5+16t6
Factor out the GCF of 4 from the expression 320r3t3.
4(5r3)+4(15r2t)+4(15rt2)+4(5t3)+4(4r6)+4(24r5t)+4(60r4t2)+4(80r3t3)+240r2t4+96rt5+16t6
Factor out the GCF of 4 from the expression 240r2t4.
4(5r3)+4(15r2t)+4(15rt2)+4(5t3)+4(4r6)+4(24r5t)+4(60r4t2)+4(80r3t3)+4(60r2t4)+96rt5+16t6
Factor out the GCF of 4 from the expression 96rt5.
4(5r3)+4(15r2t)+4(15rt2)+4(5t3)+4(4r6)+4(24r5t)+4(60r4t2)+4(80r3t3)+4(60r2t4)+4(24rt5)+16t6
Factor out the GCF of 4 from the expression 16t6.
4(5r3)+4(15r2t)+4(15rt2)+4(5t3)+4(4r6)+4(24r5t)+4(60r4t2)+4(80r3t3)+4(60r2t4)+4(24rt5)+4(4t6)
4(5r3)+4(15r2t)+4(15rt2)+4(5t3)+4(4r6)+4(24r5t)+4(60r4t2)+4(80r3t3)+4(60r2t4)+4(24rt5)+4(4t6)
Since all the terms share a common factor of 4, it can be factored out of each term.
4(5r3+15r2t+15rt2+5t3+4r6+24r5t+60r4t2+80r3t3+60r2t4+24rt5+4t6)
4(5r3+15r2t+15rt2+5t3+4r6+24r5t+60r4t2+80r3t3+60r2t4+24rt5+4t6)
Step 3
The greatest common factor GCF is the term in front of the factored expression.
4